seidel signless laplacian energy of graphs

Let s(g) be the seidel matrix of a graph g of order n and let ds (g) = diag(n − 1 − 2d1, n − 1 − 2d2, . . . , n − 1 − 2dn) be the diagonal matrix with di denoting the degree of a vertex vi in g. the seidel laplacian matrix of g is defined as sl(g) = ds (g) − s(g) and the seidel signless laplacian matrix as sl+(g) = ds (g) + s(g). the seidel signless laplacian energy esl+ (g) is defined as the sum of the absolute deviations of the eigenvalues of sl+(g) from their mean. in this paper, we establish the main properties of the eigenvalues of sl+(g) and of esl+ (g).