The Distance Laplacian Spectral Radius of Clique Trees

Abstract

The distance Laplacian matrix of a connected graph G is defined as ℒG=TrG−DG, where DG is the distance matrix of G and TrG is the diagonal matrix of vertex transmissions of G. The largest eigenvalue of ℒG is called the distance Laplacian spectral radius of G. In this paper, we determine the graphs with maximum and minimum distance Laplacian spectral radius among all clique trees with n vertices and k cliques. Moreover, we obtainn vertices and k cliques.