{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T10:26:16Z","timestamp":1768731976436,"version":"3.49.0"},"reference-count":11,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":7802,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1985,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper presents some results regarding the design of reliable networks. The problem under consideration involves networks which are undirected graphs having equal and independent edge failure probabilities. The index of reliability is the probability that the network fails (becomes disconnected). For \u201csmall\u201d edge failure probabilities and given <jats:italic>p<\/jats:italic> and <jats:italic>q<\/jats:italic> there exists a class of <jats:italic>p<\/jats:italic> vertex, <jats:italic>q<\/jats:italic> edge graphs with the property that any graph in the class has a smaller probability of disconnection than any graph outside of the class. We solve the problem of synthesizing graphs in this class.<\/jats:p>","DOI":"10.1002\/net.3230150210","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T19:20:34Z","timestamp":1178911234000},"page":"257-271","source":"Crossref","is-referenced-by-count":68,"title":["Combinatorial optimization problems in the analysis and design of probabilistic networks"],"prefix":"10.1002","volume":"15","author":[{"given":"D.","family":"Bauer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"Boesch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Suffel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"Tindell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230130210"},{"key":"e_1_2_1_3_2","first-page":"45","volume-title":"The Theory and Applications of Graphs","author":"Bauer D.","year":"1981"},{"key":"e_1_2_1_4_2","unstructured":"D.Bauer F.Boesch C.SuffelandR.Van Slyke On the validity of a reduction of reliable network design to a graph extremal problem. Operations Research (submitted)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230020306"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190080406"},{"key":"e_1_2_1_7_2","article-title":"Super line\u2010connectivity properties of circulant graphs","author":"Boesch F.","journal-title":"SIAM J. Alg. & Discrete Methods"},{"key":"e_1_2_1_8_2","unstructured":"F.Boesch andJ.Wang A class of maximally reliable networks with minimum transmission delay. IEEE Trans on Circuits and Systems (submitted)."},{"key":"e_1_2_1_9_2","volume-title":"Graph Algorithms","author":"Even S.","year":"1979"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.48.7.1142"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1137\/0212053"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230150210","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230150210","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T21:22:43Z","timestamp":1697836963000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230150210"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,6]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1985,6]]}},"alternative-id":["10.1002\/net.3230150210"],"URL":"https:\/\/doi.org\/10.1002\/net.3230150210","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,6]]}}}