Group for Research in Decision Analysis

# Distance Laplacian eigenvalues and chromatic number in graphs

## Mustapha Aouchiche and Pierre Hansen

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 $$\chi$$. We prove lower bounds on the distance Laplacian spectral radius in terms of $$n$$ and $$\chi$$. We also prove results related to the distribution of the distance Laplacian eigenvalues with respect to the values of the chromatic number $$\chi$$. For some of the results, we characterize the extremal graphs, for others, we give examples of extremal graphs.

, 14 pages