Bounds on the entries of the principal eigenvector of the distance signless Laplacian matrix

The distance signless Laplacian spectral radius of a connected graph G is the largest eigenvalue of the distance signless Laplacian matrix of G  , defined as DQ(G)=Tr(G)+D(G)DQ(G)=Tr(G)+D(G), where D(G)D(G) is the distance matrix of G   and Tr(G)Tr(G) is the diagonal matrix of vertex transmissions of G  . In this paper we determine upper and lower bounds on the minimal and maximal entries of the principal eigenvector of DQ(G)DQ(G) and characterize the extremal graphs. In addition, we obtain a lower bound on the distance signless Laplacian spectral radius of G based on its order and independence number, and characterize the extremal graph.