{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T03:12:47Z","timestamp":1719803567242},"reference-count":10,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2015,2,4]],"date-time":"2015-02-04T00:00:00Z","timestamp":1423008000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2015,12]]},"abstract":"Abstract<\/jats:title>A set S<\/jats:italic> of vertices in a graph G<\/jats:italic> is an independent dominating set of G<\/jats:italic> if S<\/jats:italic> is an independent set and every vertex not in S<\/jats:italic> is adjacent to a vertex in\u00a0S<\/jats:italic>. The independent domination number of G<\/jats:italic>, denoted by\u00a0, is the minimum cardinality of an independent dominating set. In this article, we show that if is a connected cubic graph of order\u00a0n<\/jats:italic> that does not have a subgraph isomorphic to K<\/jats:italic>2, 3<\/jats:sub>, then . As a consequence of our main result, we deduce Reed's important result [Combin Probab Comput 5 (1996), 277\u2013295] that if G<\/jats:italic> is a cubic graph of order\u00a0n<\/jats:italic>, then , where denotes the domination number of G<\/jats:italic>.<\/jats:p>","DOI":"10.1002\/jgt.21855","type":"journal-article","created":{"date-parts":[[2015,2,4]],"date-time":"2015-02-04T06:15:22Z","timestamp":1423030522000},"page":"329-349","source":"Crossref","is-referenced-by-count":14,"title":["Independent Domination in Cubic Graphs"],"prefix":"10.1002","volume":"80","author":[{"given":"Paul","family":"Dorbec","sequence":"first","affiliation":[{"name":"UNIVERSITY OF BORDEAUX, LABRI UMR5800, F\u201033405 Talence, France CNRS, LABRI, UMR5800 F\u201033405 TALENCE FRANCE"}]},{"given":"Michael A.","family":"Henning","sequence":"additional","affiliation":[{"name":"DEPARTMENT OF MATHEMATICS UNIVERSITY OF JOHANNESBURG AUCKLAND PARK 2006 SOUTH AFRICA"}]},{"given":"Mickael","family":"Montassier","sequence":"additional","affiliation":[{"name":"UNIVERSITY OF MONTPELLIER, LIRMM UMR5506, MONTPELLIER FRANCE"}]},{"given":"Justin","family":"Southey","sequence":"additional","affiliation":[{"name":"DEPARTMENT OF MATHEMATICS UNIVERSITY OF JOHANNESBURG AUCKLAND PARK 2006 SOUTH AFRICA"}]}],"member":"311","published-online":{"date-parts":[[2015,2,4]]},"reference":[{"key":"e_1_2_5_2_1","first-page":"411","volume-title":"Proceedings of the Eight Quadrennial International Conference of Graph Theory, Combinatorics, Algorithms, and Applications","author":"Fischer D. C.","year":"1999"},{"key":"e_1_2_5_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2012.11.031"},{"key":"e_1_2_5_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00026-012-0155-4"},{"key":"e_1_2_5_5_1","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"e_1_2_5_6_1","volume-title":"Domination in Graphs: Advanced Topics","author":"Haynes T. W.","year":"1998"},{"key":"e_1_2_5_7_1","unstructured":"A.Kelmans Counterexamples to the cubic graph domination conjecture arXiv:math.CO\/0607512 v1 20 July 2006."},{"key":"e_1_2_5_8_1","first-page":"465","article-title":"A new bound on the domination number of connected cubic graphs","volume":"6","author":"Kostochka A. V.","year":"2009","journal-title":"Sib Elektron Mat Izv"},{"key":"e_1_2_5_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199908)31:4<297::AID-JGT4>3.0.CO;2-1"},{"key":"e_1_2_5_10_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300002042"},{"key":"e_1_2_5_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(98)00350-1"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.21855","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.21855","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T21:26:11Z","timestamp":1696368371000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.21855"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,4]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,12]]}},"alternative-id":["10.1002\/jgt.21855"],"URL":"https:\/\/doi.org\/10.1002\/jgt.21855","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,4]]}}}