{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:29:00Z","timestamp":1759638540198},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2009,9]]},"abstract":"<jats:p> For a graph G with n vertices and a permutation \u03b1 on V(G), a permutation graph P<jats:sub>\u03b1<\/jats:sub>(G) is obtained from two identical copies of G by adding an edge between v and \u03b1(V) for any v \u03f5 V(G). Let \u03b3(G) be the domination number of a graph G. It has been shown that \u03b3(G) \u2264 \u03b3(P<jats:sub>\u03b1<\/jats:sub>(G) \u2264 2\u03b3(G) for any permutation \u03b1 on V(G). In this paper, we investigate specific graphs for which there exists a permutation \u03b1 such that \u03b3(P<jats:sub>\u03b1<\/jats:sub>(G)) \u227b \u03b3(G) in terms of the domination number of G or the maximum degree of G. Additionally, we construct a class of graphs for which the domination number of any permutation graph is twice the domination number of the original graph, as well as explore finding a specific graph G and permutation \u03b1 for any two positive integers a and b with a \u2264 b \u2264 2a, to have \u03b3(G) = a and \u03b3(P<jats:sub>\u03b1<\/jats:sub>(G)) = b. <\/jats:p>","DOI":"10.1142\/s0219265909002522","type":"journal-article","created":{"date-parts":[[2009,9,23]],"date-time":"2009-09-23T11:33:52Z","timestamp":1253705632000},"page":"205-217","source":"Crossref","is-referenced-by-count":2,"title":["BOUNDS ON THE DOMINATION NUMBER OF PERMUTATION GRAPHS"],"prefix":"10.1142","volume":"10","author":[{"given":"WEIZHEN","family":"GU","sequence":"first","affiliation":[{"name":"Mathematics Department, Texas State University, 601 University Drive, San Marcos, TX 78666, USA"}]},{"given":"KIRSTI","family":"WASH","sequence":"additional","affiliation":[{"name":"Mathematics Department, Texas State University, 601 University Drive, San Marcos, TX 78666, USA"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","unstructured":"M.\u00a0Borowiecki, Recent Advances in Graph Theory (Academia, Prague, 1975)\u00a0pp. 89\u201392."},{"key":"rf3","unstructured":"G.\u00a0Chartrand and J.\u00a0Frechen, Proof Techniques in Graph Theory (Academic Press, New York, 1969)\u00a0pp. 21\u201324."},{"key":"rf4","first-page":"433","volume":"3","author":"Chartrand G.","journal-title":"Ann. Inst. H. Poincare Sec. B(N. S.)"},{"key":"rf5","first-page":"33","volume":"44","author":"Ellingham M.","journal-title":"Congr. Numer."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.11.006"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0037(199905)33:3<161::AID-NET1>3.0.CO;2-3"},{"key":"rf10","volume-title":"Fundamentals of Domination In Graphs","author":"Haynes T.","year":"1998"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(91)90047-Z"},{"key":"rf15","first-page":"143","volume":"49","author":"Piazza B.","journal-title":"Cong. Numer."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(84)90007-4"},{"key":"rf17","volume-title":"Introduction To Graph Theory","author":"West D.","year":"2001"},{"key":"rf18","first-page":"193","volume":"23","author":"Zelinka B.","journal-title":"Mat. Casopis Sloven. Akad. Vied"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219265909002522","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T13:57:37Z","timestamp":1565099857000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219265909002522"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9]]},"references-count":12,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,4,30]]},"published-print":{"date-parts":[[2009,9]]}},"alternative-id":["10.1142\/S0219265909002522"],"URL":"https:\/\/doi.org\/10.1142\/s0219265909002522","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"value":"0219-2659","type":"print"},{"value":"1793-6713","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9]]}}}