{"title":"有向图的斜拉普拉斯(斜邻接)谱半径的边界","authors":"H. A. Ganie","doi":"10.22108/TOC.2019.112589.1582","DOIUrl":null,"url":null,"abstract":"For a simple connected graph $G$ with $n$ vertices and $m$ edges, let $overrightarrow{G}$ be a digraph obtained by giving an arbitrary direction to the edges of $G$. In this paper, we consider the skew Laplacian/skew adjacency matrix of the digraph $overrightarrow{G}$. We obtain upper bounds for the skew Laplacian/skew adjacency spectral radius, in terms of various parameters (like oriented degree, average oriented degree) associated with the structure of the digraph $overrightarrow{G}$. We also obtain upper and lower bounds for the skew Laplacian/skew adjacency spectral radius, in terms of skew Laplacian/skew adjacency rank of the digraph $overrightarrow{G}$.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"8 1","pages":"1-12"},"PeriodicalIF":0.6000,"publicationDate":"2019-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Bounds for the skew Laplacian (skew adjacency) spectral radius of a digraph\",\"authors\":\"H. A. Ganie\",\"doi\":\"10.22108/TOC.2019.112589.1582\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a simple connected graph $G$ with $n$ vertices and $m$ edges, let $overrightarrow{G}$ be a digraph obtained by giving an arbitrary direction to the edges of $G$. In this paper, we consider the skew Laplacian/skew adjacency matrix of the digraph $overrightarrow{G}$. We obtain upper bounds for the skew Laplacian/skew adjacency spectral radius, in terms of various parameters (like oriented degree, average oriented degree) associated with the structure of the digraph $overrightarrow{G}$. We also obtain upper and lower bounds for the skew Laplacian/skew adjacency spectral radius, in terms of skew Laplacian/skew adjacency rank of the digraph $overrightarrow{G}$.\",\"PeriodicalId\":43837,\"journal\":{\"name\":\"Transactions on Combinatorics\",\"volume\":\"8 1\",\"pages\":\"1-12\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2019-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions on Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/TOC.2019.112589.1582\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2019.112589.1582","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Bounds for the skew Laplacian (skew adjacency) spectral radius of a digraph
For a simple connected graph $G$ with $n$ vertices and $m$ edges, let $overrightarrow{G}$ be a digraph obtained by giving an arbitrary direction to the edges of $G$. In this paper, we consider the skew Laplacian/skew adjacency matrix of the digraph $overrightarrow{G}$. We obtain upper bounds for the skew Laplacian/skew adjacency spectral radius, in terms of various parameters (like oriented degree, average oriented degree) associated with the structure of the digraph $overrightarrow{G}$. We also obtain upper and lower bounds for the skew Laplacian/skew adjacency spectral radius, in terms of skew Laplacian/skew adjacency rank of the digraph $overrightarrow{G}$.