Inverse sum indeg energy of graphs

Abstract

Suppose G is an n-vertex simple graph with vertex set {v1, . . ., vn} and di, i = 1, . . ., n, is the degree of vertex vi in G. The ISI matrix S(G) = [sij]n×n of G is defined by sij = ddi+iddjj 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 by n P |τi|, where τi are the S-eigenvalues. We give ISI energy formula of some graph classes. We also obtain i=1 some bounds for ISI energy of graphs. In the end, we give some noncospectral equienergetic graphs with respect to inverse sum indeg energy.