{"title":"顶点分割图中的距离支配","authors":"A. Frendrup, Z. Tuza, P. Vestergaard","doi":"10.1556/314.2022.00006","DOIUrl":null,"url":null,"abstract":"We treat a variation of graph domination which involves a partition (V\n 1, V\n 2,..., Vk\n ) of the vertex set of a graph G and domination of each partition class V\n i over distance d where all vertices and edges of G may be used in the domination process. Strict upper bounds and extremal graphs are presented; the results are collected in three handy tables. Further, we compare a high number of partition classes and the number of dominators needed.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"22 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Distance Domination in Vertex Partitioned Graphs\",\"authors\":\"A. Frendrup, Z. Tuza, P. Vestergaard\",\"doi\":\"10.1556/314.2022.00006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We treat a variation of graph domination which involves a partition (V\\n 1, V\\n 2,..., Vk\\n ) of the vertex set of a graph G and domination of each partition class V\\n i over distance d where all vertices and edges of G may be used in the domination process. Strict upper bounds and extremal graphs are presented; the results are collected in three handy tables. Further, we compare a high number of partition classes and the number of dominators needed.\",\"PeriodicalId\":383314,\"journal\":{\"name\":\"Mathematica Pannonica\",\"volume\":\"22 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-03-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica Pannonica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1556/314.2022.00006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Pannonica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1556/314.2022.00006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We treat a variation of graph domination which involves a partition (V
1, V
2,..., Vk
) of the vertex set of a graph G and domination of each partition class V
i over distance d where all vertices and edges of G may be used in the domination process. Strict upper bounds and extremal graphs are presented; the results are collected in three handy tables. Further, we compare a high number of partition classes and the number of dominators needed.
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