Inverse sum indeg energy of graphs

Abstract

Suppose G is an n-vertex simple graph with vertex set {v1,..., vn} and d(i), i = 1,..., n, is the degree of vertex vi in G. The ISI matrix S(G) = [sij] of G is a square matrix of order n and is defined by sij = d(i)d(j)/d(i)+d(j) if the vertices vi and vj are adjacent and sij = 0 otherwise. The S-eigenvalues of G are the eigenvalues of its ISI matrix S(G). Recently the notion of inverse sum indeg (henceforth, ISI) energy of graphs is introduced and is defined as the sum of absolute values of S-eigenvalues of graph G. We give ISI energy formula of some graph classes. We also obtain some bounds for ISI energy of graphs.