{"title":"论符号图的幂","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":"{\"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}","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}
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.