{"title":"TOTAL DOMINATION INTEGRITY OF WHEEL RELATED GRAPHS","authors":"N. H. Shah, P. L. Vihol","doi":"10.17654/0974165823009","DOIUrl":null,"url":null,"abstract":"The total domination integrity of a simple connected graph G with no isolated vertices is denoted by TDI(G) and defined as TDI(G)=min { left | S right |+m(G-S) : S subseteq V(G) }, where S is a total dominating set of G and m(G - S) is the order of a maximum connected component of G - S. It is a new measure of vulnerability of a graph. This work is aimed to discuss total domination integrity of wheel, gear, helm, closed helm, flower graph, web graph, sunflower graph and web graph without center.","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-01-25","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/10.17654/0974165823009","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
The total domination integrity of a simple connected graph G with no isolated vertices is denoted by TDI(G) and defined as TDI(G)=min { left | S right |+m(G-S) : S subseteq V(G) }, where S is a total dominating set of G and m(G - S) is the order of a maximum connected component of G - S. It is a new measure of vulnerability of a graph. This work is aimed to discuss total domination integrity of wheel, gear, helm, closed helm, flower graph, web graph, sunflower graph and web graph without center.
无孤立顶点的简单连通图G的总控制完整性用TDI(G)表示，定义为TDI(G)=min{左| S右|+m(G-S): S subseteq V(G)}，其中S为G的总控制集，m(G-S)为G-S的最大连通分量的阶数，是一种新的图的脆弱性度量。本研究旨在探讨轮、齿轮、舵、闭舵、花图、网图、向日葵图和无中心网图的总体控制完整性。
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