Distance Laplacian eigenvalues and chromatic number in graphs

Abstract

In the present paper we are interested in the study of the distance Laplacian eigenvalues of a connected graph with fixed order n and chromatic number x. We prove lower bounds on the distance Laplacian spectral radius in terms of n and x. We also prove results related to the distribution of the distance Laplacian eigenvalues with respect to the values of the chromatic number x. For some of the results, we characterize the extremal graphs, for others, we give examples of extremal graphs.