NoorA’lawiah Abd Aziz, Nader Jafari Rad, H. Kamarulhaili
{"title":"关于三角盘的支配","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":" ","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":\" \",\"pages\":\"\"},\"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}","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}
. 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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