{"title":"On the Connectivities of the Generalized Line, Middle and Total Graph","authors":"T. Hamada, Tai-ichi Kitamura, I. Yoshimura","doi":"10.5036/BFSIU1968.7.47","DOIUrl":null,"url":null,"abstract":"We investigate the generalized line graph, total graph and middle graph of the given graphs. First, replace a given graph G with a multigraph M having the same point set as G, then it constructs the total graph T(G) from G. Two suitable subgraphs Mx(G), Lx(G), of Tx(G) are considered as extensions of middle graph M(G) and line graph L(G) respectively.We also consider the connectivities of graphs which are obtained as a special case of Lx(G), Mx(G) and Tx(G). Then we get some extensions of established theorems.","PeriodicalId":141145,"journal":{"name":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","volume":"75 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1975-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/BFSIU1968.7.47","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
We investigate the generalized line graph, total graph and middle graph of the given graphs. First, replace a given graph G with a multigraph M having the same point set as G, then it constructs the total graph T(G) from G. Two suitable subgraphs Mx(G), Lx(G), of Tx(G) are considered as extensions of middle graph M(G) and line graph L(G) respectively.We also consider the connectivities of graphs which are obtained as a special case of Lx(G), Mx(G) and Tx(G). Then we get some extensions of established theorems.