{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:05:45Z","timestamp":1740107145802,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2018,9,5]],"date-time":"2018-09-05T00:00:00Z","timestamp":1536105600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-170450-2013","RGPIN 2017-04401"],"award-info":[{"award-number":["RGPIN-170450-2013","RGPIN 2017-04401"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2018,11]]},"DOI":"10.1007\/s00373-018-1946-0","type":"journal-article","created":{"date-parts":[[2018,9,5]],"date-time":"2018-09-05T14:42:14Z","timestamp":1536158534000},"page":"1445-1457","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Graphs for Independence and k-Independence Polynomials"],"prefix":"10.1007","volume":"34","author":[{"given":"J. I.","family":"Brown","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3432-0083","authenticated-orcid":false,"given":"D.","family":"Cox","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,9,5]]},"reference":[{"key":"1946_CR1","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1017\/S0269964800143074","volume":"14","author":"Y Ath","year":"2011","unstructured":"Ath, Y., Sobel, M.: Some conjectured uniformly optimal reliable networks. Probab. Eng. Inform. Sci. 14, 375\u2013383 (2011)","journal-title":"Probab. Eng. Inform. Sci."},{"key":"1946_CR2","first-page":"1","volume":"14","author":"J Culter","year":"2000","unstructured":"Culter, J., Radcliffe, A.J.: Extremal problems for independent set enumeration. Electr. J. Comb. 14, 1\u201317 (2000)","journal-title":"Electr. J. Comb."},{"key":"1946_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-44205-0","volume-title":"Proofs from The Book","author":"M Aigner","year":"2014","unstructured":"Aigner, M., Ziegler, G.M.: Proofs from The Book, 5th edn. Springer, New York (2014)","edition":"5"},{"key":"1946_CR4","doi-asserted-by":"publisher","first-page":"2004","DOI":"10.1109\/26.61483","volume":"38","author":"FT Boesch","year":"1990","unstructured":"Boesch, F.T., Satyanarayana, A., Suffel, C.L.: Least reliable networks and the reliability domination. IEEE Trans. Comm. 38, 2004\u20132009 (1990)","journal-title":"IEEE Trans. Comm."},{"key":"1946_CR5","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1002\/net.3230210204","volume":"21","author":"F Boesch","year":"1991","unstructured":"Boesch, F., Li, X., Suffel, C.: On the existence of uniformly optimally reliable networks. Networks 21, 181\u2013194 (1991)","journal-title":"Networks"},{"key":"1946_CR6","volume-title":"Extremal Graph Theory","author":"B Bollob\u00e1s","year":"1978","unstructured":"Bollob\u00e1s, B.: Extremal Graph Theory. Academic Press, London (1978)"},{"key":"1946_CR7","volume-title":"Discrete Structures and Their Interactions","author":"JI Brown","year":"2013","unstructured":"Brown, J.I.: Discrete Structures and Their Interactions. CRC, Boca Raton (2013)"},{"key":"1946_CR8","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1002\/net.21530","volume":"63","author":"JI Brown","year":"2014","unstructured":"Brown, J.I., Cox, D.: Nonexistence of optimal graphs for all terminal reliability. Networks 63, 146\u2013153 (2014)","journal-title":"Networks"},{"key":"1946_CR9","doi-asserted-by":"publisher","first-page":"2292","DOI":"10.1016\/j.disc.2008.05.003","volume":"309","author":"JI Brown","year":"2009","unstructured":"Brown, J.I., Hoshino, R.: Independence polynomials of circulants with an application to music. Discrete Math. 309, 2292\u20132304 (2009)","journal-title":"Discrete Math."},{"key":"1946_CR10","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)"},{"key":"1946_CR11","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1002\/(SICI)1097-0037(199807)31:4<217::AID-NET2>3.0.CO;2-G","volume":"31","author":"D Gross","year":"1998","unstructured":"Gross, D., Saccoman, J.T.: Uniformly optimal reliable graphs. Networks 31, 217\u2013225 (1998)","journal-title":"Networks"},{"key":"1946_CR12","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1017\/S0027763000006930","volume":"153","author":"J Herzog","year":"1999","unstructured":"Herzog, J., Hibi, T.: Componentwise Linear Ideals. Nagoya Math. J. 153, 141\u2013159 (1999)","journal-title":"Nagoya Math. J."},{"key":"1946_CR13","unstructured":"Hoefel, A.: Hilbert Functions in Monomial Algebras, Ph.D. Disseratation, Dalhousie University (2011)"},{"key":"1946_CR14","first-page":"97","volume":"24","author":"I Gutman","year":"1983","unstructured":"Gutman, I., Harary, F.: Generalizations of the matching polynomial. Utilitas Mathematica 24, 97\u2013106 (1983)","journal-title":"Utilitas Mathematica"},{"key":"1946_CR15","first-page":"187","volume-title":"Theory of Graphs","author":"G Katona","year":"1966","unstructured":"Katona, G.: A Theorem of finite sets. In: Erd\u00f6s, P., Katona, G. (eds.) Theory of Graphs, pp. 187\u2013207. Akademia Kiad\u00f3, Budapest (1966)"},{"key":"1946_CR16","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1525\/9780520319875-014","volume-title":"Mathematical Optimization Techniques","author":"JB Kruskal","year":"1963","unstructured":"Kruskal, J.B.: The number of simplicies in a complex. In: Bellman, R. (ed.) Mathematical Optimization Techniques, pp. 251\u2013278. University of California Press, Berkeley (1963)"},{"key":"1946_CR17","unstructured":"Levit, V.E.: The independence polynomial of a graph\u2014a survey. In: Bozapalidis, S., Kalampakas, A., Rahonis, G. (eds.) Proceedings of the First Annual Conference on Algebraic Informatics, pp. 233\u2013254. Aristotle University of Thessaloniki, Greece (2005)"},{"key":"1946_CR18","first-page":"431","volume":"15","author":"L Lov\u00e1sz","year":"1976","unstructured":"Lov\u00e1sz, L., Simonovits, M.: On the number of complete subgraphs of a graph. Congr. Numer. 15, 431\u2013441 (1976)","journal-title":"Congr. Numer."},{"key":"1946_CR19","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1112\/plms\/s2-26.1.531","volume":"26","author":"R Macaulay","year":"1927","unstructured":"Macaulay, R.: Some Properties of Enumeration in Theory of Modular Systems. Proc. Lond. Math. Soc. 26, 531\u2013555 (1927)","journal-title":"Proc. Lond. Math. Soc."},{"key":"1946_CR20","unstructured":"Mermin, J.: Lexicographic Ideals, Ph.D. Dissertation, Cornell University (2006)"},{"key":"1946_CR21","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1002\/net.3230210404","volume":"21","author":"W Myrvold","year":"1991","unstructured":"Myrvold, W., Cheung, K.H., Page, L.B., Perry, J.E.: Uniformly most reliable networks do not always exist. Networks 21, 417\u2013419 (1991)","journal-title":"Networks"},{"key":"1946_CR22","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1002\/jgt.3190190407","volume":"19","author":"A Sakaloglu","year":"1995","unstructured":"Sakaloglu, A., Satyanarayana, A.: Graphs with the least number of colourings. J. Graph Theory 19, 523\u2013533 (1995)","journal-title":"J. Graph Theory"},{"issue":"11","key":"1946_CR23","doi-asserted-by":"publisher","first-page":"2228","DOI":"10.1016\/j.disc.2007.04.069","volume":"308","author":"I Simonelli","year":"2008","unstructured":"Simonelli, I.: Optimal graphs for chromatic polynomials. Discrete Math. 308(11), 2228\u20132239 (2008)","journal-title":"Discrete Math."},{"key":"1946_CR24","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1002\/sapm1975542135","volume":"54","author":"RP Stanley","year":"1975","unstructured":"Stanley, R.P.: The upper bound conjecture and cohen-macaulay rings. Stud. Appl. Math. 54, 135\u2013142 (1975)","journal-title":"Stud. Appl. Math."},{"key":"1946_CR25","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/0012-365X(90)90202-S","volume":"82","author":"D Fisher","year":"1990","unstructured":"Fisher, D., Solow, A.: Dependence polynomials. Discrete Math. 82, 251\u2013258 (1990)","journal-title":"Discrete Math."},{"key":"1946_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-75859-4","volume-title":"Simplicial Complexes of Graphs","author":"J Jonsson","year":"2008","unstructured":"Jonsson, J.: Simplicial Complexes of Graphs. Springer, New York (2008)"}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00373-018-1946-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-018-1946-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-018-1946-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T22:00:41Z","timestamp":1693864841000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00373-018-1946-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,5]]},"references-count":26,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,11]]}},"alternative-id":["1946"],"URL":"https:\/\/doi.org\/10.1007\/s00373-018-1946-0","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"type":"print","value":"0911-0119"},{"type":"electronic","value":"1435-5914"}],"subject":[],"published":{"date-parts":[[2018,9,5]]},"assertion":[{"value":"10 October 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 August 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 September 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}