On incidence energy of graphs

Abstract

Let G=(V,E) be a simple graph with vertex set V={v1,v2,…,vn} and edge set E={e1,e2,…,em}. The incidence matrix I(G) of G is the n×m matrix whose (i,j)-entry is 1 if vi is incident to ej and 0 otherwise. The incidence energy IE of G is the sum of the singular values of I(G). In this paper we give lower and upper bounds for IE in terms of n, m, maximum degree, clique number, independence number, and the first Zagreb index. Moreover, we obtain Nordhaus–Gaddum-type results for IE.