LAUSR

Abstract Let G a graph on n vertices. The signless Laplacian matrix of G, denoted by Q ( G ) , is defined as Q ( G ) = D ( G ) + A ( G ) , where A ( G ) is the adjacency matrix of G and D ( G ) is the diagonal matrix of the degrees of G. A graph G is said to be Q-integral if all eigenvalues of the matrix Q ( G ) are integers. In this paper, we characterize all Q-integral graphs among all connected graphs with at most two vertices of degree greater than or equal to three.