On the distance Laplacian spectral radius of bipartite graphs

Suppose that the vertex set of a graph G is V(G) = {v(1), ... v(n)}. Then we denote by Tr-G(v(i)) the sum of distances between v(i) and other vertices of G. Let Tr (G) be the n x n diagonal matrix with its (i, i)-entry equal to Tr-G(v(i)) and D(G) be the distance matrix of G. Then L-D(G) = Tr (G) - D(G) is the distance Laplacian matrix of G. The distance Laplacian spectral radius of G is the spectral radius of L-D(G). In this paper we describe the unique graph with minimum distance Laplacian spectral radius among all connected bipartite graphs of order n with a given matching number and a given vertex connectivity, respectively. (C) 2015 Elsevier B.V. All rights reserved.