<![CDATA[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.]]>
Copyrights © 2019
