On the distance signless Laplacian spectral radius of graphs

The distance signless Laplacian spectral radius of a connected graph G is the spectral radius of the distance signless Laplacian matrix of G, defined as Q(G) = Tr(G) + D(G), where Tr(G) is the diagonal matrix of vertex transmissions of G and D(G) is the distance matrix of G. In this paper, we determine the graphs with minimum distance signless Laplacian spectral radius among the trees, unicyclic graphs and bipartite graphs with fixed numbers of vertices, respectively, and determine the graphs with minimum distance signless Laplacian spectral radius among the connected graphs with fixed numbers of vertices and pendant vertices, and the connected graphs with fixed number of vertices and connectivity, respectively.