{"title":"与某些图类相关的矩阵的群逆","authors":"J. McDonald, R. Nandi, K. Sivakumar","doi":"10.13001/ela.2022.6717","DOIUrl":null,"url":null,"abstract":"We obtain formulae for group inverses of matrices that are associated with a new class of digraphs obtained from stars. This new class contains both bipartite and non-bipartite graphs. Expressions for the group inverse of matrices corresponding to double star digraphs and the adjacency matrix of certain undirected multi-star graphs are also proven. A blockwise representation of the inverse or group inverse of the adjacency matrix of the Dutch windmill graph is presented.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Group inverses of matrices associated with certain graph classes\",\"authors\":\"J. McDonald, R. Nandi, K. Sivakumar\",\"doi\":\"10.13001/ela.2022.6717\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We obtain formulae for group inverses of matrices that are associated with a new class of digraphs obtained from stars. This new class contains both bipartite and non-bipartite graphs. Expressions for the group inverse of matrices corresponding to double star digraphs and the adjacency matrix of certain undirected multi-star graphs are also proven. A blockwise representation of the inverse or group inverse of the adjacency matrix of the Dutch windmill graph is presented.\",\"PeriodicalId\":50540,\"journal\":{\"name\":\"Electronic Journal of Linear Algebra\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-03-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Linear Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.13001/ela.2022.6717\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Linear Algebra","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.13001/ela.2022.6717","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
Group inverses of matrices associated with certain graph classes
We obtain formulae for group inverses of matrices that are associated with a new class of digraphs obtained from stars. This new class contains both bipartite and non-bipartite graphs. Expressions for the group inverse of matrices corresponding to double star digraphs and the adjacency matrix of certain undirected multi-star graphs are also proven. A blockwise representation of the inverse or group inverse of the adjacency matrix of the Dutch windmill graph is presented.
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