Laplacian SumEccentricity Energy of a Graph

We introduce the Laplacian sum-eccentricity matrix LSe of a graph G, and its Laplacian sum-eccentricity energy LSeE = n i i ζi − 2m 1 2 n i=1 |η |, where η = e n and where ζ , ζ , . . . , ζ are the eigenvalues of LS . Upper bounds for LSeE are obtained. A graph is said to be twinenergetic if n i i=1 |η | = n i=1 |ζi|. Conditions for the existence of such graphs are established.