{"title":"具有四个和五个不同的无符号拉普拉斯特征值的树","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":"{\"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}","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}
Trees with Four and Five Distinct Signless Laplacian Eigenvalues
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.