{"title":"产品图形的主导着色","authors":"Minhui Li, Shumin Zhang, Chengfu Ye","doi":"10.1007/s10878-023-01094-7","DOIUrl":null,"url":null,"abstract":"<p>The dominated coloring (dom-coloring) of a graph <i>G</i> is a proper coloring such that each color class is dominated by at least one vertex. The dominated chromatic number (dom-chromatic number) of <i>G</i> is the minimum number of color classes among all dominated colorings of <i>G</i>, denoted by <span>\\(\\chi _{\\text {dom}}(G)\\)</span>. In this paper, we study the dominated coloring of Cartesian product, direct product, lexicographic product and strong product of some graphs.\n</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dominated coloring in product graphs\",\"authors\":\"Minhui Li, Shumin Zhang, Chengfu Ye\",\"doi\":\"10.1007/s10878-023-01094-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The dominated coloring (dom-coloring) of a graph <i>G</i> is a proper coloring such that each color class is dominated by at least one vertex. The dominated chromatic number (dom-chromatic number) of <i>G</i> is the minimum number of color classes among all dominated colorings of <i>G</i>, denoted by <span>\\\\(\\\\chi _{\\\\text {dom}}(G)\\\\)</span>. In this paper, we study the dominated coloring of Cartesian product, direct product, lexicographic product and strong product of some graphs.\\n</p>\",\"PeriodicalId\":50231,\"journal\":{\"name\":\"Journal of Combinatorial Optimization\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-11-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10878-023-01094-7\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10878-023-01094-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
The dominated coloring (dom-coloring) of a graph G is a proper coloring such that each color class is dominated by at least one vertex. The dominated chromatic number (dom-chromatic number) of G is the minimum number of color classes among all dominated colorings of G, denoted by \(\chi _{\text {dom}}(G)\). In this paper, we study the dominated coloring of Cartesian product, direct product, lexicographic product and strong product of some graphs.
期刊介绍:
The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering.
The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.