NoorA’lawiah Abd Aziz, Nader Jafari Rad, H. Kamarulhaili
{"title":"On the domination of triangulated discs","authors":"NoorA’lawiah Abd Aziz, Nader Jafari Rad, H. Kamarulhaili","doi":"10.21136/mb.2022.0122-21","DOIUrl":null,"url":null,"abstract":". Let G be a 3-connected triangulated disc of order n with the boundary cycle C of the outer face of G . Tokunaga (2013) conjectured that G has a dominating set of cardinality at most 14 ( n +2). This conjecture is proved in Tokunaga (2020) for G − C being a tree. In this paper we prove the above conjecture for G − C being a unicyclic graph. We also deduce some bounds for the double domination number, total domination number and double total domination number in triangulated discs.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Bohemica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21136/mb.2022.0122-21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
. Let G be a 3-connected triangulated disc of order n with the boundary cycle C of the outer face of G . Tokunaga (2013) conjectured that G has a dominating set of cardinality at most 14 ( n +2). This conjecture is proved in Tokunaga (2020) for G − C being a tree. In this paper we prove the above conjecture for G − C being a unicyclic graph. We also deduce some bounds for the double domination number, total domination number and double total domination number in triangulated discs.
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