{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T22:05:04Z","timestamp":1778796304086,"version":"3.51.4"},"reference-count":47,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2007,3,9]],"date-time":"2007-03-09T00:00:00Z","timestamp":1173398400000},"content-version":"vor","delay-in-days":8590,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1983,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For a noncomplete graph <jats:italic>G<\/jats:italic>, the traditional definition of its connectivity is the minimum number of points whose removal results in a disconnected subgraph with components <jats:italic>H<\/jats:italic><jats:sub>1<\/jats:sub>,\u2026,<jats:italic>H<jats:sub>k<\/jats:sub><\/jats:italic>. The conditional connectivity of <jats:italic>G<\/jats:italic> with respect to some graph\u2010theoretic property <jats:italic>P<\/jats:italic> is the smallest cardinality of a set <jats:italic>S<\/jats:italic> of points, if any, such that every component <jats:italic>H<jats:sub>i<\/jats:sub><\/jats:italic> of the disconnected graph <jats:italic>G<\/jats:italic> \u2010 <jats:italic>S<\/jats:italic> has property <jats:italic>P.<\/jats:italic> A survey of promising properties <jats:italic>P<\/jats:italic> is presented. Questions for various <jats:italic>P<\/jats:italic>\u2010connectivities are listed in analogy with known results on connectivity and line\u2010connectivity.<\/jats:p>","DOI":"10.1002\/net.3230130303","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T16:17:49Z","timestamp":1178900269000},"page":"347-357","source":"Crossref","is-referenced-by-count":407,"title":["Conditional connectivity"],"prefix":"10.1002","volume":"13","author":[{"given":"Frank","family":"Harary","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,3,9]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1155\/S016117127900020X"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190060214"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579300003806"},{"key":"e_1_2_1_5_2","unstructured":"F. T.Boesch An introduction to the theory of large\u2010scale networks. InLarge\u2010Scale Networks: Theory and Design.IEEE New York (1976) pp.3\u201310."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230110106"},{"key":"e_1_2_1_7_2","article-title":"Circulants and their connectivities","author":"Boesch F.","journal-title":"J. Graph Theory."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9967-7"},{"key":"e_1_2_1_9_2","volume-title":"Extremal Graph Theory","author":"Bollob\u00e1s B.","year":"1978"},{"key":"e_1_2_1_10_2","first-page":"281","article-title":"Extremal graphs with given diameter and connectivity","volume":"1","author":"Bollob\u00e1s B.","year":"1976","journal-title":"Ars Combin."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1137\/1003061"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1137\/0114065"},{"key":"e_1_2_1_13_2","first-page":"61","volume-title":"Theory of Graphs","author":"Chartrand G.","year":"1968"},{"key":"e_1_2_1_14_2","first-page":"4252","article-title":"G\u00e9n\u00e9ralisations du th\u00e9or\u00e9me de Menger","volume":"250","author":"Dirac G. A.","year":"1967","journal-title":"C. R. Acad. Sci."},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230120405"},{"key":"e_1_2_1_16_2","doi-asserted-by":"crossref","first-page":"184","DOI":"10.7146\/math.scand.a-11910","article-title":"The crossing numbers of some generalized Petersen graphs","volume":"48","author":"Exoo G.","year":"1981","journal-title":"Math. Scand."},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1956-045-5"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400875184"},{"key":"e_1_2_1_19_2","first-page":"105","volume-title":"Springer Lecture Notes Math","author":"Geller D. P.","year":"1971"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(79)90132-8"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01226435"},{"key":"e_1_2_1_22_2","volume-title":"Structural Models in Anthropology","author":"Hage P.","year":"1983"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-10.37.26"},{"key":"e_1_2_1_24_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.48.7.1142"},{"key":"e_1_2_1_25_2","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"e_1_2_1_26_2","first-page":"3","article-title":"What are mathematical models and what should they be","volume":"12","author":"Harary F.","year":"1971","journal-title":"Biom. Praxim."},{"key":"e_1_2_1_27_2","article-title":"Maximum versus minimum invariants for graphs","author":"Harary F.","journal-title":"J. Graph Theory."},{"key":"e_1_2_1_28_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1979.tb32800.x"},{"key":"e_1_2_1_29_2","first-page":"101","article-title":"Extremal graphs with given connectivities","volume":"2","author":"Harary F.","year":"1978","journal-title":"South East Asian Bull. Math."},{"key":"e_1_2_1_30_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230100308"},{"key":"e_1_2_1_31_2","unstructured":"F.HararyandV.Malyshko Blockade flows in networks. Unpublished."},{"key":"e_1_2_1_32_2","first-page":"67","article-title":"On the measure of connectedness in a social group","volume":"15","author":"Harary F.","year":"1970","journal-title":"Gen. Syst."},{"key":"e_1_2_1_33_2","volume-title":"Structural Models: An Introduction to the Theory of Directed Graphs","author":"Harary F.","year":"1965"},{"key":"e_1_2_1_34_2","volume-title":"Graphical Enumeration","author":"Harary F.","year":"1973"},{"key":"e_1_2_1_35_2","doi-asserted-by":"publisher","DOI":"10.2307\/2786017"},{"key":"e_1_2_1_36_2","first-page":"325","article-title":"Planar composite graphs","volume":"32","author":"Harary F.","year":"1971","journal-title":"An. Acad. Brasil. Ci."},{"key":"e_1_2_1_37_2","first-page":"88","article-title":"Every forest can be obtained from a minimal block","volume":"323","author":"Harary F.","year":"1981","journal-title":"J. Reine Angew. Math."},{"key":"e_1_2_1_38_2","doi-asserted-by":"publisher","DOI":"10.1137\/0114024"},{"key":"e_1_2_1_39_2","volume-title":"A Mathematician's Apology","author":"Hardy G. H.","year":"1940"},{"key":"e_1_2_1_40_2","doi-asserted-by":"publisher","DOI":"10.2307\/2034282"},{"key":"e_1_2_1_41_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-10-1-96-115"},{"key":"e_1_2_1_42_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190050402"},{"key":"e_1_2_1_43_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1968-0228369-8"},{"key":"e_1_2_1_44_2","article-title":"Min\u2010max relations for directed graphs","volume":"13","author":"Schrijver A.","year":"1982","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_1_45_2","first-page":"436","article-title":"An extremal problem in graph theory (in Hungarian)","volume":"48","author":"Tur\u00e1n P.","year":"1941","journal-title":"Mat. Fiz. Lapok"},{"key":"e_1_2_1_46_2","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-22.2.107"},{"key":"e_1_2_1_47_2","volume-title":"The Connectivity of Graphs","author":"Tutte W. T.","year":"1967"},{"key":"e_1_2_1_48_2","doi-asserted-by":"publisher","DOI":"10.2307\/2371086"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230130303","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230130303","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T22:54:28Z","timestamp":1697756068000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230130303"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,9]]},"references-count":47,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1983,9]]}},"alternative-id":["10.1002\/net.3230130303"],"URL":"https:\/\/doi.org\/10.1002\/net.3230130303","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,9]]}}}