Praba Venkatrengan, Swaminathan Venkatasubramanian, R. Sundareswaran
{"title":"Dominator semi strong color partition in graphs","authors":"Praba Venkatrengan, Swaminathan Venkatasubramanian, R. Sundareswaran","doi":"10.31801/cfsuasmas.1014919","DOIUrl":null,"url":null,"abstract":"Let GG =(V,E)(V,E) be a simple graph. A subset SS is said to be Semi-Strong if for every vertex vv in VV, |N(v)∩S|≤1|N(v)∩S|≤1, or no two vertices of SS have the same neighbour in VV, that is, no two vertices of SS are joined by a path of length two in VV. The minimum cardinality of a semi-strong partition of GG is called the semi-strong chromatic number of GG and is denoted by χsGχsG. A proper colour partition is called a dominator colour partition if every vertex dominates some colour class, that is , every vertex is adjacent with every element of some colour class. In this paper, instead of proper colour partition, semi-strong colour partition is considered and every vertex is adjacent to some class of the semi-strong colour partition.Several interesting results are obtained.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31801/cfsuasmas.1014919","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let GG =(V,E)(V,E) be a simple graph. A subset SS is said to be Semi-Strong if for every vertex vv in VV, |N(v)∩S|≤1|N(v)∩S|≤1, or no two vertices of SS have the same neighbour in VV, that is, no two vertices of SS are joined by a path of length two in VV. The minimum cardinality of a semi-strong partition of GG is called the semi-strong chromatic number of GG and is denoted by χsGχsG. A proper colour partition is called a dominator colour partition if every vertex dominates some colour class, that is , every vertex is adjacent with every element of some colour class. In this paper, instead of proper colour partition, semi-strong colour partition is considered and every vertex is adjacent to some class of the semi-strong colour partition.Several interesting results are obtained.