Group for Research in Decision Analysis

# Connections between eigenvalues and chromatic number in graphs

## Mustapha Aouchiche – UAE University, UAE

In the present talk, we are interested in the distance Laplacian eigenvalues of a connected graph with fixed order $$n$$ and chromatic number $$\chi$$. We provide lower bounds on the distance Laplacian spectral radius in terms of $$n$$ and $$\chi$$. We also discuss 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.

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