Groupe d’études et de recherche en analyse des décisions

G-2011-78

A Signless Laplacian for the Distance Matrix of a Graph

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We introduce a signless Laplacian for the distance matrix of a connected graph, called the distance signless Laplacian. We study the distance signless Laplacian spectrum of a connected graph. We show the equivalence between the distance signless Laplacian, distance Laplacian and the distance spectra for the class of transmission regular graphs. We also establish a relationship between the smallest eigenvalue of the distance signless Laplacian of a connected graph G and the existence of a bipartite component in the complement .

, 16 pages