{"title":"The [1,2]-set properties and algorithm analysis of tree","authors":"Chao Zhang, Tao Chen","doi":"10.1117/12.3031908","DOIUrl":null,"url":null,"abstract":"A set S⊆V(G) in graph G is a [j, k]-set if it satisfies that G[S] is a subgraph of G and each vertex v∈V(G)∖S, has j≤∣N(v)∩S∣≤k, wherein j and k are nonnegative integers. In this paper, we focus on the situation of j=1, k=2, that is, [1,2]-set of graph G. We mainly study the situation of γ(T)-set and γ[1,2](T)-set in tree, and analyse a particular tree called spider. Then discuss with two different algorithm to calculate the [1,2]-domination number γ[1,2](T) in tree. Finally, compare and analyze the calculation results.","PeriodicalId":342847,"journal":{"name":"International Conference on Algorithms, Microchips and Network Applications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Conference on Algorithms, Microchips and Network Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1117/12.3031908","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A set S⊆V(G) in graph G is a [j, k]-set if it satisfies that G[S] is a subgraph of G and each vertex v∈V(G)∖S, has j≤∣N(v)∩S∣≤k, wherein j and k are nonnegative integers. In this paper, we focus on the situation of j=1, k=2, that is, [1,2]-set of graph G. We mainly study the situation of γ(T)-set and γ[1,2](T)-set in tree, and analyse a particular tree called spider. Then discuss with two different algorithm to calculate the [1,2]-domination number γ[1,2](T) in tree. Finally, compare and analyze the calculation results.
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