{"title":"一类完全图的开包装数","authors":"K. R. Chandrasekar, S. Saravanakumar","doi":"10.15826/umj.2020.2.004","DOIUrl":null,"url":null,"abstract":"Let \\(G\\) be a graph with the vertex set \\(V(G)\\). A subset \\(S\\) of \\(V(G)\\) is an open packing set of \\(G\\) if every pair of vertices in \\(S\\) has no common neighbor in \\(G.\\) The maximum cardinality of an open packing set of \\(G\\) is the open packing number of \\(G\\) and it is denoted by \\(\\rho^o(G)\\). In this paper, the exact values of the open packing numbers for some classes of perfect graphs, such as split graphs, \\(\\{P_4, C_4\\}\\)-free graphs, the complement of a bipartite graph, the trestled graph of a perfect graph are obtained.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"OPEN PACKING NUMBER FOR SOME CLASSES OF PERFECT GRAPHS\",\"authors\":\"K. R. Chandrasekar, S. Saravanakumar\",\"doi\":\"10.15826/umj.2020.2.004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let \\\\(G\\\\) be a graph with the vertex set \\\\(V(G)\\\\). A subset \\\\(S\\\\) of \\\\(V(G)\\\\) is an open packing set of \\\\(G\\\\) if every pair of vertices in \\\\(S\\\\) has no common neighbor in \\\\(G.\\\\) The maximum cardinality of an open packing set of \\\\(G\\\\) is the open packing number of \\\\(G\\\\) and it is denoted by \\\\(\\\\rho^o(G)\\\\). In this paper, the exact values of the open packing numbers for some classes of perfect graphs, such as split graphs, \\\\(\\\\{P_4, C_4\\\\}\\\\)-free graphs, the complement of a bipartite graph, the trestled graph of a perfect graph are obtained.\",\"PeriodicalId\":36805,\"journal\":{\"name\":\"Ural Mathematical Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ural Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15826/umj.2020.2.004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ural Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15826/umj.2020.2.004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
OPEN PACKING NUMBER FOR SOME CLASSES OF PERFECT GRAPHS
Let \(G\) be a graph with the vertex set \(V(G)\). A subset \(S\) of \(V(G)\) is an open packing set of \(G\) if every pair of vertices in \(S\) has no common neighbor in \(G.\) The maximum cardinality of an open packing set of \(G\) is the open packing number of \(G\) and it is denoted by \(\rho^o(G)\). In this paper, the exact values of the open packing numbers for some classes of perfect graphs, such as split graphs, \(\{P_4, C_4\}\)-free graphs, the complement of a bipartite graph, the trestled graph of a perfect graph are obtained.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
