{"title":"On self-graphoidal graphs and their complements","authors":"Karam Ratan Singh , S. Pirzada","doi":"10.1016/j.kjs.2024.100267","DOIUrl":null,"url":null,"abstract":"<div><p>The graphoidal graph <span><math><mi>G</mi></math></span> of graph <span><math><mi>H</mi></math></span> is the graph obtained by taking graphoidal cover <span><math><mi>Ψ</mi></math></span> of <span><math><mi>H</mi></math></span> as vertices and two vertices are adjacent if and only if the corresponding paths have a non-empty intersection. If <span><math><mi>G</mi></math></span> is isomorphic to one of its graphoidal graphs, then <span><math><mi>G</mi></math></span> is said to be a self-graphoidal graph. <span><math><mi>G</mi></math></span> is called self-complementary graphoidal graph if it is isomorphic to one of its complementary graphoidal graphs. In this article, we characterize self-graphoidal graphs and give a construction of self-graphoidal graphs from cycle and wheel graphs. Also, we give a characterization of self-complementary graphoidal graphs.</p></div>","PeriodicalId":17848,"journal":{"name":"Kuwait Journal of Science","volume":"51 4","pages":"Article 100267"},"PeriodicalIF":1.2000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2307410824000920/pdfft?md5=cd72229fa5e87963b32a12a90aa267b4&pid=1-s2.0-S2307410824000920-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kuwait Journal of Science","FirstCategoryId":"103","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2307410824000920","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
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Abstract
The graphoidal graph of graph is the graph obtained by taking graphoidal cover of as vertices and two vertices are adjacent if and only if the corresponding paths have a non-empty intersection. If is isomorphic to one of its graphoidal graphs, then is said to be a self-graphoidal graph. is called self-complementary graphoidal graph if it is isomorphic to one of its complementary graphoidal graphs. In this article, we characterize self-graphoidal graphs and give a construction of self-graphoidal graphs from cycle and wheel graphs. Also, we give a characterization of self-complementary graphoidal graphs.
图 H 的类图形 G 是以 H 的类图形盖 Ψ 为顶点得到的图形，当且仅当对应路径有非空交集时，两个顶点相邻。如果 G 与其中一个图形同构，则称 G 为自图形。如果 G 与其中一个互补图形同构，则称 G 为自互补图形。在本文中，我们将描述自形图的特征，并给出从循环图和车轮图构建自形图的方法。此外，我们还给出了自互补图形的特征。
期刊介绍：
Kuwait Journal of Science (KJS) is indexed and abstracted by major publishing houses such as Chemical Abstract, Science Citation Index, Current contents, Mathematics Abstract, Micribiological Abstracts etc. KJS publishes peer-review articles in various fields of Science including Mathematics, Computer Science, Physics, Statistics, Biology, Chemistry and Earth & Environmental Sciences. In addition, it also aims to bring the results of scientific research carried out under a variety of intellectual traditions and organizations to the attention of specialized scholarly readership. As such, the publisher expects the submission of original manuscripts which contain analysis and solutions about important theoretical, empirical and normative issues.
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