{"title":"关于第 II 组的共最大子群图","authors":"Angsuman Das, Manideepa Saha","doi":"10.1007/s11587-023-00836-3","DOIUrl":null,"url":null,"abstract":"<p>In this sequel paper, we continue our study on co-maximal subgroup graph <span>\\(\\Gamma (G)\\)</span> of a group <i>G</i>. We discuss some further results on connectedness and when <span>\\(\\Gamma (G)\\)</span> is edgeless. Moreover, we study the independence number, chromatic number and perfectness of <span>\\(\\Gamma (G)\\)</span>. In the process, we show that if the independence number is suitably small, then the underlying group is solvable. We also classify co-maximal subgroup graphs of certain groups upto isomorphism.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On co-maximal subgroup graph of a group-II\",\"authors\":\"Angsuman Das, Manideepa Saha\",\"doi\":\"10.1007/s11587-023-00836-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this sequel paper, we continue our study on co-maximal subgroup graph <span>\\\\(\\\\Gamma (G)\\\\)</span> of a group <i>G</i>. We discuss some further results on connectedness and when <span>\\\\(\\\\Gamma (G)\\\\)</span> is edgeless. Moreover, we study the independence number, chromatic number and perfectness of <span>\\\\(\\\\Gamma (G)\\\\)</span>. In the process, we show that if the independence number is suitably small, then the underlying group is solvable. We also classify co-maximal subgroup graphs of certain groups upto isomorphism.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-12-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11587-023-00836-3\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11587-023-00836-3","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
In this sequel paper, we continue our study on co-maximal subgroup graph \(\Gamma (G)\) of a group G. We discuss some further results on connectedness and when \(\Gamma (G)\) is edgeless. Moreover, we study the independence number, chromatic number and perfectness of \(\Gamma (G)\). In the process, we show that if the independence number is suitably small, then the underlying group is solvable. We also classify co-maximal subgroup graphs of certain groups upto isomorphism.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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