The Sum-Eccentricity Energy of A Graph

Abstract

In this paper, we introduce the concept of the sum-eccentricity matrix of a graph and obtain some coefficients of the characteristic polynomial of the sum-eccentricity matrix of . We also introduce the sum-eccentricity energy of a graph . Sum-eccentricity energies of some well-known graphs are obtained. Upper and lower bounds for are estblished. It is shown that if the sum-eccentricity energy of a graph is rational then it must be an even.