{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T02:30:14Z","timestamp":1768012214076,"version":"3.49.0"},"reference-count":86,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,6,21]],"date-time":"2018-06-21T00:00:00Z","timestamp":1529539200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math.Comput.Sci."],"published-print":{"date-parts":[[2018,9]]},"DOI":"10.1007\/s11786-018-0345-5","type":"journal-article","created":{"date-parts":[[2018,6,21]],"date-time":"2018-06-21T05:46:13Z","timestamp":1529559973000},"page":"275-293","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":45,"title":["Sixty Years of Network Reliability"],"prefix":"10.1007","volume":"12","author":[{"given":"Hebert","family":"P\u00e9rez-Ros\u00e9s","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,6,21]]},"reference":[{"issue":"5","key":"345_CR1","doi-asserted-by":"publisher","first-page":"1525","DOI":"10.1109\/TNET.2012.2232111","volume":"21","author":"PK Agarwal","year":"2013","unstructured":"Agarwal, P.K., et al.: The resilience of WDM networks to probabilistic geographical failures. IEEE\/ACM Trans. Netw. 21(5), 1525\u20131538 (2013)","journal-title":"IEEE\/ACM Trans. Netw."},{"issue":"3","key":"345_CR2","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1002\/net.3230210307","volume":"21","author":"AT Amin","year":"1991","unstructured":"Amin, A.T., Siegrist, K.T., Slater, P.J.: On the nonexistence of uniformly optimal graphs for pair-connected reliability. Networks 21(3), 359\u2013368 (1991)","journal-title":"Networks"},{"issue":"3","key":"345_CR3","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1002\/net.3230230306","volume":"23","author":"AT Amin","year":"1993","unstructured":"Amin, A.T., Siegrist, K.T., Slater, P.J.: On uniformly optimally reliable graphs for pairconnected reliability with vertex failures. Networks 23(3), 185\u2013193 (1993)","journal-title":"Networks"},{"key":"345_CR4","series-title":"Dover Books on Mathematics","volume-title":"Combinatorics of Finite Sets","author":"I Anderson","year":"1987","unstructured":"Anderson, I.: Combinatorics of Finite Sets. Dover Books on Mathematics. Dover, New York (1987). ISBN: 9780486422572"},{"issue":"2","key":"345_CR5","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1137\/0603016","volume":"3","author":"MO Ball","year":"1982","unstructured":"Ball, M.O., Scott Provan, J.: Bounds on the reliability polynomial for shellable independence systems. SIAM J. Algebr. Discrete Methods 3(2), 166\u2013181 (1982)","journal-title":"SIAM J. Algebr. Discrete Methods"},{"issue":"2","key":"345_CR6","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1002\/net.3230130210","volume":"13","author":"MO Ball","year":"1983","unstructured":"Ball, M.O., Scott Provan, J.: Calculating bounds on reachability and connectedness in stochastic networks. Networks 13(2), 253\u2013278 (1983)","journal-title":"Networks"},{"issue":"2","key":"345_CR7","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1016\/j.orl.2014.12.014","volume":"43","author":"J Barrera","year":"2015","unstructured":"Barrera, J., Cancela, H., Moreno, E.: Topological optimization of reliable networks under dependent failures. Oper. Res. Lett. 43(2), 132\u2013136 (2015)","journal-title":"Oper. Res. Lett."},{"key":"345_CR8","doi-asserted-by":"crossref","unstructured":"Boesch, F.T.: On the synthesis of optimally reliable networks having unreliable nodes but reliable edges. In: INFOCOM \u201988. Networks: Evolution or Revolution, Proceedings of the Seventh Annual Joint Conference of the IEEE Computer and Communcations Societies, pp. 829\u2013834. IEEE (1988)","DOI":"10.1109\/INFCOM.1988.12997"},{"issue":"3","key":"345_CR9","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/0166-218X(88)90065-0","volume":"21","author":"TB Brecht","year":"1988","unstructured":"Brecht, T.B., Colbourn, C.J.: Lower bounds on two-terminal network reliability. Discrete Appl. Math. 21(3), 185\u2013198 (1988)","journal-title":"Discrete Appl. Math."},{"issue":"3","key":"345_CR10","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1002\/net.21697","volume":"68","author":"J Brown","year":"2016","unstructured":"Brown, J., Mol, L.: On the roots of the node reliability polynomial. Networks 68(3), 238\u2013246 (2016)","journal-title":"Networks"},{"key":"345_CR11","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.dam.2014.05.048","volume":"177","author":"JI Brown","year":"2014","unstructured":"Brown, J.I., Cox, D., Ehrenborg, R.: The average reliability of a graph. Discrete Appl. Math. 177, 19\u201333 (2014)","journal-title":"Discrete Appl. Math."},{"issue":"2","key":"345_CR12","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1002\/net.20148","volume":"49","author":"JI Brown","year":"2007","unstructured":"Brown, J.I., Li, X.: Uniformly optimal digraphs for strongly connected reliability. Networks 49(2), 145\u2013151 (2007)","journal-title":"Networks"},{"key":"345_CR13","doi-asserted-by":"crossref","unstructured":"Bulka, D., Dugan, J.B.: A lower bound on the reliability of an n-dimensional hypercube. In: Proceedings Ninth Symposium on Reliable Distributed Systems, pp. 44\u201353 (1990)","DOI":"10.1109\/RELDIS.1990.93950"},{"issue":"1","key":"345_CR14","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1109\/24.285106","volume":"43","author":"D Bulka","year":"1994","unstructured":"Bulka, D., Dugan, J.B.: Network s\u2013t reliability bounds using a 2-dimensional reliability polynomial. IEEE Trans. Reliab. 43(1), 39\u201345 (1994)","journal-title":"IEEE Trans. Reliab."},{"key":"345_CR15","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.dam.2015.06.005","volume":"198","author":"JM Burgos","year":"2016","unstructured":"Burgos, J.M.: Factorization of network reliability with perfect nodes II: connectivity matrix. Discrete Appl. Math. 198, 91\u2013100 (2016)","journal-title":"Discrete Appl. Math."},{"key":"345_CR16","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.dam.2015.06.006","volume":"198","author":"JM Burgos","year":"2016","unstructured":"Burgos, J.M., Amoza, F.R.: Factorization of network reliability with perfect nodes I: introduction and statements. Discrete Appl. Math. 198, 82\u201390 (2016)","journal-title":"Discrete Appl. Math."},{"issue":"4","key":"345_CR17","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1002\/net.21654","volume":"66","author":"E Canale","year":"2015","unstructured":"Canale, E., et al.: Diameter constrained reliability: complexity, distinguished topologies and asymptotic behavior. Networks 66(4), 296\u2013305 (2015)","journal-title":"Networks"},{"issue":"5","key":"345_CR18","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1111\/itor.12159","volume":"22","author":"E Canale","year":"2015","unstructured":"Canale, E., et al.: Full complexity analysis of the diameter-constrained reliability. Int. Trans. Oper. Res. 22(5), 811\u2013821 (2015)","journal-title":"Int. Trans. Oper. Res."},{"issue":"1","key":"345_CR19","doi-asserted-by":"publisher","first-page":"17","DOI":"10.2298\/YJOR140721004C","volume":"26","author":"H Cancela","year":"2016","unstructured":"Cancela, H., et al.: Diameter constrained reliability of ladders and Spanish fans. Yugosl. J. Oper. Res. 26(1), 17\u201332 (2016)","journal-title":"Yugosl. J. Oper. Res."},{"issue":"2","key":"345_CR20","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1109\/TR.2004.829152","volume":"53","author":"Y Chen","year":"2004","unstructured":"Chen, Y., He, Z.: Bounds on the reliability of distributed systems with unreliable nodes and links. IEEE Trans. Reliab. 53(2), 205\u2013215 (2004)","journal-title":"IEEE Trans. Reliab."},{"issue":"1","key":"345_CR21","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/0012-365X(88)90193-8","volume":"72","author":"CJ Colbourn","year":"1988","unstructured":"Colbourn, C.J.: Edge-packing of graphs and network reliability. Discrete Math. 72(1), 49\u201361 (1988)","journal-title":"Discrete Math."},{"issue":"3","key":"345_CR22","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1137\/0608033","volume":"8","author":"CJ Colbourn","year":"1987","unstructured":"Colbourn, C.J.: Network resilience. SIAM J. Algebr. Discrete Methods 8(3), 404\u2013409 (1987)","journal-title":"SIAM J. Algebr. Discrete Methods"},{"key":"345_CR23","volume-title":"The Combinatorics of Network Reliability","author":"CJ Colbourn","year":"1987","unstructured":"Colbourn, C.J.: The Combinatorics of Network Reliability. Oxford University Press, New York (1987). ISBN 0-19-504920-9"},{"issue":"3","key":"345_CR24","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1016\/0016-0032(93)90102-Z","volume":"330","author":"CJ Colbourn","year":"1993","unstructured":"Colbourn, C.J., Harms, D.D., Myrvold, W.J.: Reliability polynomials can cross twice. J. Frankl. Inst. 330(3), 629\u2013633 (1993)","journal-title":"J. Frankl. Inst."},{"issue":"1","key":"345_CR25","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.laa.2006.08.017","volume":"423","author":"NMM Abreu de","year":"2007","unstructured":"de Abreu, N.M.M.: Old and new results on algebraic connectivity of graphs. Linear Algebra Appl. 423(1), 53\u201373 (2007)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"345_CR26","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1002\/net.3230190106","volume":"19","author":"LL Doty","year":"1989","unstructured":"Doty, L.L.: Extremal connectivity and vulnerability in graphs. Networks 19(1), 73\u201378 (1989)","journal-title":"Networks"},{"issue":"5","key":"345_CR27","doi-asserted-by":"publisher","first-page":"568","DOI":"10.1002\/nav.20245","volume":"54","author":"MR Dugas","year":"2007","unstructured":"Dugas, M.R., Samaniego, F.J.: On optimal system designs in reliability-economics frameworks. Nav. Res. Logist. 54(5), 568\u2013582 (2007)","journal-title":"Nav. Res. Logist."},{"issue":"1","key":"345_CR28","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1109\/71.80187","volume":"2","author":"A El-Amawy","year":"1991","unstructured":"El-Amawy, A., Latifi, S.: Properties and performance of folded hypercubes. IEEE Trans. Parallel Distrib. Syst. 2(1), 31\u201342 (1991)","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"issue":"10","key":"345_CR29","doi-asserted-by":"publisher","first-page":"2491","DOI":"10.1016\/j.laa.2011.02.024","volume":"435","author":"W Ellens","year":"2011","unstructured":"Ellens, W., et al.: Effective graph resistance. Linear Algebra Appl. 435(10), 2491\u20132506 (2011)","journal-title":"Linear Algebra Appl."},{"key":"345_CR30","doi-asserted-by":"crossref","unstructured":"Elspas, B.: Topological constraints on interconnection-limited logic. In: 1964 Proceedings of the Fifth Annual Symposium on Switching Circuit Theory and Logical Design, pp. 133\u2013137 (1964)","DOI":"10.1109\/SWCT.1964.27"},{"issue":"2","key":"345_CR31","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1002\/net.3230160208","volume":"16","author":"T Evans","year":"1986","unstructured":"Evans, T., Smith, D.: Optimally reliable graphs for both edge and vertex failures. Networks 16(2), 199\u2013204 (1986)","journal-title":"Networks"},{"issue":"2","key":"345_CR32","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1002\/net.3230120204","volume":"12","author":"O Frank","year":"1982","unstructured":"Frank, O., Gaul, W.: On reliability in stochastic graphs. Networks 12(2), 119\u2013126 (1982)","journal-title":"Networks"},{"key":"345_CR33","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-06440-6","volume-title":"Ternary Networks: Reliability and Monte Carlo","author":"I Gertsbakh","year":"2014","unstructured":"Gertsbakh, I., Shpungin, Y., Vaisman, R.: Ternary Networks: Reliability and Monte Carlo. Springer, Berlin (2014). ISBN 3319064398"},{"key":"345_CR34","volume-title":"Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo","author":"IB Gertsbakh","year":"2009","unstructured":"Gertsbakh, I.B., Shpungin, Y.: Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo, 1st edn. CRC Press, Boca Raton (2009). ISBN: 1439817413","edition":"1"},{"key":"345_CR35","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-22374-7","volume-title":"Network Reliability and Resilience","author":"IB Gertsbakh","year":"2011","unstructured":"Gertsbakh, I.B., Shpungin, Y.: Network Reliability and Resilience. Springer, Berlin (2011). ISBN 978-3-642-22373-0"},{"issue":"4","key":"345_CR36","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1002\/net.3230240407","volume":"24","author":"O Goldschmidt","year":"1994","unstructured":"Goldschmidt, O., Jaillet, P., Lasota, R.: On reliability of graphs with node failures. Networks 24(4), 251\u2013259 (1994)","journal-title":"Networks"},{"key":"345_CR37","doi-asserted-by":"publisher","DOI":"10.1142\/8963","volume-title":"Spanning Tree Results for Graphs and Multigraphs: A Matrix-Theoretic Approach","author":"DJ Gross","year":"2014","unstructured":"Gross, D.J., Saccoman, J.T., Suffel, C.L.: Spanning Tree Results for Graphs and Multigraphs: A Matrix-Theoretic Approach. World Scientific, Singapore (2014). ISBN: 9789814566056"},{"key":"345_CR38","doi-asserted-by":"publisher","DOI":"10.1002\/9781118914410","volume-title":"Fundamentals of Reliability Engineering: Applications in Multistage Interconnection Networks","author":"I Gunawan","year":"2014","unstructured":"Gunawan, I.: Fundamentals of Reliability Engineering: Applications in Multistage Interconnection Networks. Wiley, New York (2014). ISBN: 978-1-118-54956-8"},{"issue":"3","key":"345_CR39","doi-asserted-by":"publisher","first-page":"1235","DOI":"10.1007\/s11227-013-1078-5","volume":"68","author":"L Guo","year":"2014","unstructured":"Guo, L., Guo, X.: Fault tolerance of hypercubes and folded hypercubes. J. Supercomput. 68(3), 1235\u20131240 (2014)","journal-title":"J. Supercomput."},{"key":"345_CR40","volume-title":"Network Reliability. Experiments with a Symbolic Algebra Environment","author":"DD Harms","year":"1995","unstructured":"Harms, D.D., et al.: Network Reliability. Experiments with a Symbolic Algebra Environment. CRC Press, Boca Raton (1995). ISBN: 0-8493-3980-4"},{"issue":"5","key":"345_CR41","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1002\/net.3230220506","volume":"22","author":"XD Hu","year":"1992","unstructured":"Hu, X.D., Hwang, F.K.: Reliabilities of chordal rings. Networks 22(5), 487\u2013501 (1992)","journal-title":"Networks"},{"key":"345_CR42","doi-asserted-by":"crossref","unstructured":"Hu, X.D., Hwang, F.K.: Survival reliabilities of double loop networks. In: Global Telecommunications Conference, 1990, and Exhibition. \u2018Communications: Connecting the Future\u2019 (GLOBECOM\u201990), vol.2, pp. 674\u2013677. IEEE (1990)","DOI":"10.1109\/GLOCOM.1990.116593"},{"issue":"5","key":"345_CR43","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1002\/net.3230230502","volume":"23","author":"XD Hu","year":"1993","unstructured":"Hu, X.D., Hwang, F.K., Li, W.-C.I.W.: Most reliable double loop networks in survival reliability. Networks 23(5), 451\u2013458 (1993)","journal-title":"Networks"},{"issue":"12","key":"345_CR44","doi-asserted-by":"publisher","first-page":"1468","DOI":"10.1109\/12.477253","volume":"44","author":"FK Hwang","year":"1995","unstructured":"Hwang, F.K., Wright, P.E.: Survival reliability of some double-loop networks and chordal rings. IEEE Trans. Comput. 44(12), 1468\u20131471 (1995)","journal-title":"IEEE Trans. Comput."},{"issue":"1","key":"345_CR45","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/S0304-3975(01)00341-3","volume":"299","author":"FK Hwang","year":"2003","unstructured":"Hwang, F.K.: A survey on multi-loop networks. Theoret. Comput. Sci. 299(1), 107\u2013121 (2003)","journal-title":"Theoret. Comput. Sci."},{"issue":"3","key":"345_CR46","doi-asserted-by":"publisher","first-page":"255272","DOI":"10.1017\/S0269964800002072","volume":"5","author":"FK Hwang","year":"1991","unstructured":"Hwang, F.K., Li, W.-C.W.: Reliabilities of double-loop networks. Probab. Eng. Inf. Sci. 5(3), 255272 (1991)","journal-title":"Probab. Eng. Inf. Sci."},{"issue":"2","key":"345_CR47","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1002\/(SICI)1097-0037(199709)30:2<81::AID-NET2>3.0.CO;2-G","volume":"30","author":"FK Hwang","year":"1997","unstructured":"Hwang, F.K., Wright, P.E., Hu, X.D.: Exact reliabilities of most reliable double-loop networks. Networks 30(2), 81\u201390 (1997)","journal-title":"Networks"},{"key":"345_CR48","series-title":"Texts in Theoretical Computer Science. An EATCS Series","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04650-0","volume-title":"Extremal Combinatorics: With Applications in Computer Science","author":"S Jukna","year":"2001","unstructured":"Jukna, S.: Extremal Combinatorics: With Applications in Computer Science. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin (2001). ISBN 9783540663133"},{"issue":"1","key":"345_CR49","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/0885-064X(85)90021-4","volume":"1","author":"RM Karp","year":"1985","unstructured":"Karp, R.M., Luby, M.: Monte-Carlo algorithms for the planar multiterminal network reliability problem. J. Complex. 1(1), 45\u201364 (1985)","journal-title":"J. Complex."},{"issue":"1","key":"345_CR50","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/0012-365X(90)90297-U","volume":"80","author":"P Katerinis","year":"1990","unstructured":"Katerinis, P.: Toughness of graphs and the existence of factors. Discrete Math. 80(1), 81\u201392 (1990)","journal-title":"Discrete Math."},{"key":"345_CR51","first-page":"444","volume":"29","author":"A Kelmans","year":"1967","unstructured":"Kelmans, A.: Connectivity of probabilistic networks. Autom. Remote Control 29, 444\u2013460 (1967)","journal-title":"Autom. Remote Control"},{"key":"345_CR52","first-page":"564","volume":"26","author":"A Kelmans","year":"1965","unstructured":"Kelmans, A.: Some problems of network reliability analysis. Autom. Remote Control 26, 564\u2013573 (1965)","journal-title":"Autom. Remote Control"},{"key":"345_CR53","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1002\/andp.18471481202","volume":"148","author":"G Kirchhoff","year":"1847","unstructured":"Kirchhoff, G.: \u00dcber die Aufl\u00f6sung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Str\u00f6me gef\u00fchrt wird. Ann. Phys. 148, 497\u2013508 (1847)","journal-title":"Ann. Phys."},{"issue":"2","key":"345_CR54","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1109\/TR.2007.896770","volume":"56","author":"SY Kuo","year":"2007","unstructured":"Kuo, S.Y., Yeh, F.M., Lin, H.Y.: Efficient and exact reliability evaluation for networks with imperfect vertices. IEEE Trans. Reliab. 56(2), 288\u2013300 (2007)","journal-title":"IEEE Trans. Reliab."},{"issue":"2","key":"345_CR55","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1002\/(SICI)1097-0037(200003)35:2<109::AID-NET2>3.0.CO;2-N","volume":"35","author":"S Liu","year":"2000","unstructured":"Liu, S., Cheng, K.-H., Liu, X.: Network reliability with node failures. Networks 35(2), 109\u2013117 (2000)","journal-title":"Networks"},{"key":"345_CR56","doi-asserted-by":"crossref","unstructured":"Long, X., Tipper, D., Gomes, T.: Measuring the survivability of networks to geographic correlated failures. In: Optical Switching and Networking 14, Part 2 (2014). Special Issue on RNDM, pp. 117\u2013133 (2013)","DOI":"10.1016\/j.osn.2014.05.004"},{"issue":"10\u201312","key":"345_CR57","doi-asserted-by":"publisher","first-page":"2452","DOI":"10.1080\/03610926.2013.792353","volume":"43","author":"MP McAssey","year":"2014","unstructured":"McAssey, M.P., Samaniego, F.J.: On uniformly optimal networks: a reversal of fortune? Commun. Stat. Theory Methods 43(10\u201312), 2452\u20132467 (2014)","journal-title":"Commun. Stat. Theory Methods"},{"issue":"2","key":"345_CR58","first-page":"107","volume":"2","author":"MHS Mohamed","year":"2010","unstructured":"Mohamed, M.H.S., et al.: An efficient evaluation for the reliability upper bound of distributed systems with unreliable nodes and edges. Int. J. Eng. Technol. 2(2), 107\u2013110 (2010)","journal-title":"Int. J. Eng. Technol."},{"key":"345_CR59","unstructured":"Monakhova, E.A.: A survey on undirected circulant graphs. In: Discrete Mathematics, Algorithms and Applications 04.01 (2012), p. 1250002"},{"issue":"3","key":"345_CR60","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/0016-0032(56)90559-2","volume":"262","author":"EF Moore","year":"1956","unstructured":"Moore, E.F., Shannon, C.E.: Reliable circuits using less reliable relays. J. Frankl. Inst. 262(3), 191\u2013208 (1956)","journal-title":"J. Frankl. Inst."},{"key":"345_CR61","unstructured":"Myrvold, W.: Reliable network synthesis: some recent developments. In: Proceedings of International Conference on Graph Theory, Combinatorics, Algorithms, and Applications. vol. 2, pp. 651\u2013660 (1999)"},{"issue":"3","key":"345_CR62","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1109\/24.3752","volume":"37","author":"LB Page","year":"1988","unstructured":"Page, L.B., Perry, J.E.: A practical implementation of the factoring theorem for network reliability. IEEE Trans. Reliab. 37(3), 259\u2013267 (1988)","journal-title":"IEEE Trans. Reliab."},{"key":"345_CR63","first-page":"117","volume":"152","author":"L Petingi","year":"2001","unstructured":"Petingi, L., Rodriguez, J.: Reliability of networks with delay constraints. Congr. Numer. 152, 117\u2013123 (2001)","journal-title":"Congr. Numer."},{"issue":"3","key":"345_CR64","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/0166-218X(84)90024-6","volume":"9","author":"C Peyrat","year":"1984","unstructured":"Peyrat, C.: Diameter vulnerability of graphs. Discrete Appl. Math. 9(3), 245\u2013250 (1984)","journal-title":"Discrete Appl. Math."},{"issue":"5","key":"345_CR65","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1109\/24.61311","volume":"39","author":"T Politof","year":"1990","unstructured":"Politof, T., Satyanarayana, A.: A linear-time algorithm to compute the reliability of planar cube-free networks. IEEE Trans. Reliab. 39(5), 557\u2013563 (1990)","journal-title":"IEEE Trans. Reliab."},{"issue":"3","key":"345_CR66","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1109\/TR.1986.4335427","volume":"35","author":"T Politof","year":"1986","unstructured":"Politof, T., Satyanarayana, A.: Efficient algorithms for reliability analysis of planar networks\u2014a survey. IEEE Trans. Reliab. 35(3), 252\u2013259 (1986)","journal-title":"IEEE Trans. Reliab."},{"issue":"3","key":"345_CR67","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1137\/0215050","volume":"15","author":"SJ Provan","year":"1986","unstructured":"Provan, S.J.: The complexity of reliability computations in planar and acyclic graphs. SIAM J. Comput. 15(3), 694\u2013702 (1986)","journal-title":"SIAM J. Comput."},{"issue":"7","key":"345_CR68","doi-asserted-by":"publisher","first-page":"1433","DOI":"10.1016\/j.camwa.2009.07.019","volume":"58","author":"JA Rodriguez-Velazquez","year":"2009","unstructured":"Rodriguez-Velazquez, J.A., Kamisalic, A., Domingo-Ferrer, J.: On reliability indices of communication networks. Comput. Math. Appl. 58(7), 1433\u20131440 (2009)","journal-title":"Comput. Math. Appl."},{"key":"345_CR69","series-title":"International Series on Operations Research and Management Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-71797-5","volume-title":"System Signatures and their Applications in Engineering Reliability","author":"FJ Samaniego","year":"2007","unstructured":"Samaniego, F.J.: System Signatures and their Applications in Engineering Reliability. International Series on Operations Research and Management Science. Springer, Berlin (2007). ISBN: 978-0-387-71797-5"},{"issue":"1","key":"345_CR70","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1002\/net.3230130107","volume":"13","author":"A Satyanarayana","year":"1983","unstructured":"Satyanarayana, A., Chang, M.K.: Network reliability and the factoring theorem. Networks 13(1), 107\u2013120 (1983)","journal-title":"Networks"},{"key":"345_CR71","unstructured":"Satyanarayana, A., Tindell, R.: Efficient Algorithms for the Evaluation of Planar Network Reliability. Tech. rep. DTIC Document (1993). http:\/\/oai.dtic.mil\/oai\/oai?verb=getRecord&metadataPrefix=html&identifier=ADA263602"},{"issue":"4","key":"345_CR72","doi-asserted-by":"publisher","first-page":"818","DOI":"10.1137\/0214057","volume":"14","author":"A Satyanarayana","year":"1985","unstructured":"Satyanarayana, A., KevinWood, R.: A linear-time algorithm for computing K-terminal reliability in series-parallel networks. SIAM J. Comput. 14(4), 818\u2013832 (1985)","journal-title":"SIAM J. Comput."},{"key":"345_CR73","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198533863.001.0001","volume-title":"Network Reliability and Algebraic Structures","author":"DR Shier","year":"1991","unstructured":"Shier, D.R.: Network Reliability and Algebraic Structures. Oxford University Press, Oxford (1991)"},{"key":"345_CR74","unstructured":"Shpungin, Y.: Networks with unreliable nodes and edges: Monte Carlo lifetime estimation. Int. J. Electr. Comput. Energ. Electron. Commun. Eng. 1(3):458\u2013463. (2007). ISSN: 2010-376X"},{"issue":"1","key":"345_CR75","doi-asserted-by":"publisher","first-page":"93100","DOI":"10.1017\/S0963548300000493","volume":"2","author":"DH Smith","year":"1993","unstructured":"Smith, D.H.: Optimally reliable graphs for both vertex and edge failures. Comb. Probab. Comput. 2(1), 93100 (1993)","journal-title":"Comb. Probab. Comput."},{"issue":"2","key":"345_CR76","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/BF02073595","volume":"33","author":"DH Smith","year":"1991","unstructured":"Smith, D.H.: Optimally reliable networks. Ann. Oper. Res. 33(2), 107\u2013112 (1991)","journal-title":"Ann. Oper. Res."},{"issue":"6","key":"345_CR77","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1002\/net.3230200603","volume":"20","author":"DH Smith","year":"1990","unstructured":"Smith, D.H., Doty, L.L.: On the construction of optimally reliable graphs. Networks 20(6), 723\u2013729 (1990)","journal-title":"Networks"},{"issue":"4","key":"345_CR78","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1109\/71.273045","volume":"5","author":"S Soh","year":"1994","unstructured":"Soh, S., Rai, S., Trahan, J.L.: Improved lower bounds on the reliability of hypercube architectures. IEEE Trans. Parallel Distrib. Syst. 5(4), 364\u2013378 (1994)","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"issue":"2","key":"345_CR79","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1109\/24.87131","volume":"40","author":"OR Theologou","year":"1991","unstructured":"Theologou, O.R., Carlier, J.G.: Factoring and reductions for networks with imperfect vertices. IEEE Trans. Reliab. 40(2), 210\u2013217 (1991)","journal-title":"IEEE Trans. Reliab."},{"issue":"6","key":"345_CR80","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1016\/S0026-2714(96)00128-X","volume":"37","author":"CR Tripathy","year":"1997","unstructured":"Tripathy, C.R., Mahapatra, R.N., Misra, R.B.: Reliability analysis of hypercube multicomputers. Microelectron. Reliab. 37(6), 885\u2013891 (1997)","journal-title":"Microelectron. Reliab."},{"key":"345_CR81","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1002\/net.3230010307","volume":"1","author":"RM Slyke Van","year":"1971","unstructured":"Van Slyke, R.M., Frank, H.: Network reliability analysis: part I. Networks 1, 279\u2013290 (1971)","journal-title":"Networks"},{"issue":"3","key":"345_CR82","doi-asserted-by":"publisher","first-page":"690","DOI":"10.1137\/S0097539704446797","volume":"35","author":"D Vertigan","year":"2005","unstructured":"Vertigan, D.: The computational complexity of tutte invariants for planar graphs. SIAM J. Comput. 35(3), 690\u2013712 (2005)","journal-title":"SIAM J. Comput."},{"issue":"3","key":"345_CR83","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1109\/TR.1986.4335431","volume":"35","author":"RK Wood","year":"1986","unstructured":"Wood, R.K.: Factoring algorithms for computing k-terminal network reliability. IEEE Trans. Reliab. 35(3), 269\u2013278 (1986)","journal-title":"IEEE Trans. Reliab."},{"issue":"1","key":"345_CR84","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/j.disc.2009.08.006","volume":"310","author":"S Yu","year":"2010","unstructured":"Yu, S., Shao, F.-M., Meng, H.: Uniformly optimal graphs in some classes of graphs with node failures. Discrete Math. 310(1), 159\u2013166 (2010)","journal-title":"Discrete Math."},{"key":"345_CR85","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-4860-0","volume-title":"Network Robustness under Large-Scale Attacks","author":"Q Zhou","year":"2013","unstructured":"Zhou, Q., et al.: Network Robustness under Large-Scale Attacks. Springer, Berlin (2013). ISBN: 978- 1-4614-4859-4"},{"issue":"8","key":"345_CR86","doi-asserted-by":"publisher","first-page":"1782","DOI":"10.1016\/j.ins.2006.11.003","volume":"177","author":"Q Zhu","year":"2007","unstructured":"Zhu, Q., et al.: On reliability of the folded hypercubes. Inf. Sci. 177(8), 1782\u20131788 (2007)","journal-title":"Inf. Sci."}],"container-title":["Mathematics in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11786-018-0345-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-018-0345-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-018-0345-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,5]],"date-time":"2025-07-05T07:11:34Z","timestamp":1751699494000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11786-018-0345-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,21]]},"references-count":86,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["345"],"URL":"https:\/\/doi.org\/10.1007\/s11786-018-0345-5","relation":{},"ISSN":["1661-8270","1661-8289"],"issn-type":[{"value":"1661-8270","type":"print"},{"value":"1661-8289","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,21]]},"assertion":[{"value":"30 May 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 March 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 June 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}