Praba Venkatrengan, Swaminathan Venkatasubramanian, R. Sundareswaran
{"title":"图中的支配子半强颜色划分","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":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"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}","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}
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.