{"title":"THE ECCENTRIC HUB NUMBER OF A GRAPH","authors":"Veena Mathad","doi":"10.17654/0974165823062","DOIUrl":null,"url":null,"abstract":"A set $H \\subseteq V(G)$ is eccentric hub set of a graph $G$ if $H$ is a hub set of $G$ and also every $v \\in V(G) \\backslash H$ has an eccentric vertex in $H$. The minimal eccentric hub set with minimum cardinality is called minimum eccentric hub set. Its cardinality is eccentric hub number of $G$, denoted by $e h(G)$. In this paper, we deduce some results and bounds on this parameter. Further, we have studied about total number of minimum eccentric hub sets and eccentric hub graphs. Received: June 14, 2023; Accepted: August 2, 2023","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances and Applications in Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17654/0974165823062","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A set $H \subseteq V(G)$ is eccentric hub set of a graph $G$ if $H$ is a hub set of $G$ and also every $v \in V(G) \backslash H$ has an eccentric vertex in $H$. The minimal eccentric hub set with minimum cardinality is called minimum eccentric hub set. Its cardinality is eccentric hub number of $G$, denoted by $e h(G)$. In this paper, we deduce some results and bounds on this parameter. Further, we have studied about total number of minimum eccentric hub sets and eccentric hub graphs. Received: June 14, 2023; Accepted: August 2, 2023
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