The Distance Laplacian Spectral Radius of Clique Trees

The distance Laplacian matrix of a connected graph G is defined as L(G) = Tr(G) - D(G), where D(G) is the distance matrix of G and Tr(G) is the diagonal matrix of vertex transmissions of G. The largest eigenvalue of L(G) 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.