Distance signless Laplacian spectral radius and perfect matching in graphs and bipartite graphs

Abstract

The distance matrix $\mathcal{D}$ of a connected graph $G$ is the matrix indexed by the vertices of $G$ which entry ${\mathcal{D}}_{i,j}$ equals the distance between the vertices $v_i$ and $v_j$. The distance signless Laplacian matrix $\mathcal{Q}(G)$ of graph $G$ is defined as $\mathcal{Q}(G)=Diag(Tr)+\mathcal{D}(G)$, where $Diag(Tr)$ is the diagonal matrix of the vertex transmissions in $G$. The largest eigenvalue of $\mathcal{Q}(G)$ is called the distance signless Laplacian spectral radius of $G$, written as ${\eta }_1(G)$. And a perfect matching in a graph is a set of disadjacent edges covering every vertex of $G$. In this paper, we present two suffcient conditions in terms of the distance signless Laplacian sepectral radius for the exsitence of perfect matchings in graphs and bipatite graphs.

References in corpus (1)

• Signless Laplacian spectral radius and matching in graphs