Abstract
Using Lotker's interlacing theorem on the Laplacian eigenvalues of a graph in [3] and Wang and Belardo's interlacing theorem on the signless Laplacian eigenvalues of a graph in [4], we obtain inequalities which involve the independence number, chromatic number, Laplacian eigenvalues, and signless Laplacian eigenvalues of a graph. Moreover, using a theorem proved by Hoffman in [2] and a theorem proved by Wilf in [5], we obtain upper bounds for the total chromatic number of a graph.
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