LAUSR

The eccentricity of a vertex [Formula: see text] in a graph [Formula: see text] is the maximum distance between [Formula: see text] and any other vertex of [Formula: see text] A vertex with maximum eccentricity is called a peripheral vertex. In this paper, we study the distance signless Laplacian matrix of a connected graph [Formula: see text] with respect to peripheral vertices and define the peripheral distance signless Laplacian matrix of a graph [Formula: see text], denoted by [Formula: see text]. We then give some bounds on various eigenvalues of [Formula: see text] Moreover, we define energy in terms of [Formula: see text] and give some bounds on the energy.