{"title":"Trees with Four and Five Distinct Signless Laplacian Eigenvalues","authors":"G. Fath-Tabar, F. Taghvaee","doi":"10.22342/JIMS.25.3.557.302-313","DOIUrl":null,"url":null,"abstract":"Let $G$ be a simple graph with vertex set $V(G)=\\{v_1, v_2, \\cdots, v_n\\}$ andedge set $E(G)$.The signless Laplacian matrix of $G$ is the matrix $Q=D+A$, such that $D$ is a diagonal matrix%, indexed by the vertex set of $G$ where%$D_{ii}$ is the degree of the vertex $v_i$ and $A$ is the adjacency matrix of $G$.% where $A_{ij} = 1$ when there%is an edge from $i$ to $j$ in $G$ and $A_{ij} = 0$ otherwise.The eigenvalues of $Q$ is called the signless Laplacian eigenvalues of $G$ and denoted by $q_1$, $q_2$, $\\cdots$, $q_n$ in a graph with $n$ vertices.In this paper we characterize all trees with four and five distinct signless Laplacian eigenvalues.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2019-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Indonesian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22342/JIMS.25.3.557.302-313","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let $G$ be a simple graph with vertex set $V(G)=\{v_1, v_2, \cdots, v_n\}$ andedge set $E(G)$.The signless Laplacian matrix of $G$ is the matrix $Q=D+A$, such that $D$ is a diagonal matrix%, indexed by the vertex set of $G$ where%$D_{ii}$ is the degree of the vertex $v_i$ and $A$ is the adjacency matrix of $G$.% where $A_{ij} = 1$ when there%is an edge from $i$ to $j$ in $G$ and $A_{ij} = 0$ otherwise.The eigenvalues of $Q$ is called the signless Laplacian eigenvalues of $G$ and denoted by $q_1$, $q_2$, $\cdots$, $q_n$ in a graph with $n$ vertices.In this paper we characterize all trees with four and five distinct signless Laplacian eigenvalues.