{"title":"On the Powers of Signed Graphs","authors":"T. Shijin, A. GerminaK., K. ShahulHameed","doi":"10.22049/CCO.2021.27083.1193","DOIUrl":null,"url":null,"abstract":"A signed graph is an ordered pair $\\Sigma=(G,\\sigma),$ where $G=(V,E)$ is the underlying graph of $\\Sigma$ with a signature function $\\sigma:E\\rightarrow \\{1,-1\\}$. In this article, we define $n^{th}$ power of a signed graph and discuss some properties of these powers of signed graphs. As we can define two types of signed graphs as the power of a signed graph, necessary and sufficient conditions are given for an $n^{th}$ power of a signed graph to be unique. Also, we characterize balanced power signed graphs.","PeriodicalId":8442,"journal":{"name":"arXiv: Combinatorics","volume":"39 4","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22049/CCO.2021.27083.1193","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
A signed graph is an ordered pair $\Sigma=(G,\sigma),$ where $G=(V,E)$ is the underlying graph of $\Sigma$ with a signature function $\sigma:E\rightarrow \{1,-1\}$. In this article, we define $n^{th}$ power of a signed graph and discuss some properties of these powers of signed graphs. As we can define two types of signed graphs as the power of a signed graph, necessary and sufficient conditions are given for an $n^{th}$ power of a signed graph to be unique. Also, we characterize balanced power signed graphs.