{"title":"Γ-induced-paired Dominating Graphs of Paths","authors":"Saharath Sanguanpong, Nantapath Trakultraipruk","doi":"10.1109/ICVISP54630.2021.00048","DOIUrl":null,"url":null,"abstract":"Let D be a set of vertices of a graph G. Then D is called an induced-paired dominating set if every vertex in G is adjacent to some vertex in D and the subgraph induced by D contains only nonadjacent edges. The upper induced-paired domination number of G, denoted by $\\Gamma_{ip}(G)$, is the maximum cardinality of a minimal induced-paired dominating set of G. An induced-paired dominating set of cardinality $\\Gamma_{ip}(G)$ is called an $\\Gamma_{ip}(G)$-set. We introduce the $\\Gamma$-induced-paired dominating graph of G, denoted by $IPD_{\\Gamma}$, to be the graph whose vertex set is the set of all $\\Gamma_{ip}(G)$-sets, and two $\\Gamma_{ip}(G)$-sets are adjacent in $IPD_{\\Gamma}(G)$ if one can be obtained from the other by removing one vertex and adding another vertex of G. In this paper, we present the $\\Gamma$-induced-paired dominating graphs of all paths.","PeriodicalId":296789,"journal":{"name":"2021 5th International Conference on Vision, Image and Signal Processing (ICVISP)","volume":"99 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 5th International Conference on Vision, Image and Signal Processing (ICVISP)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICVISP54630.2021.00048","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
Let D be a set of vertices of a graph G. Then D is called an induced-paired dominating set if every vertex in G is adjacent to some vertex in D and the subgraph induced by D contains only nonadjacent edges. The upper induced-paired domination number of G, denoted by $\Gamma_{ip}(G)$, is the maximum cardinality of a minimal induced-paired dominating set of G. An induced-paired dominating set of cardinality $\Gamma_{ip}(G)$ is called an $\Gamma_{ip}(G)$-set. We introduce the $\Gamma$-induced-paired dominating graph of G, denoted by $IPD_{\Gamma}$, to be the graph whose vertex set is the set of all $\Gamma_{ip}(G)$-sets, and two $\Gamma_{ip}(G)$-sets are adjacent in $IPD_{\Gamma}(G)$ if one can be obtained from the other by removing one vertex and adding another vertex of G. In this paper, we present the $\Gamma$-induced-paired dominating graphs of all paths.