Groupe d’études et de recherche en analyse des décisions

# An Inequality for the Signless Laplacian Index of a Graph Using the Chromatic Number

## Pierre Hansen et Claire Lucas

Let Q = D + A denote the signless Laplacian matrix of a graph G of order n, where D is the diagonal matrix of the degrees and A the adjacency matrix of G. Let q1 denote the index of Q and $\chi$ the chromatic number of G. In this note we prove that $q_1 \leq 2n(1-1/\chi)$.

, 10 pages