On the oriented incidence energy and decomposable graphs

Abstract

Let G be a simple graph with n vertices and m edges. Let edges of G be given an arbitrary orientation, and let Q be the vertex-edge incidence matrix of such oriented graph. The oriented incidence energy of G is then the sum of singular values of Q. We show that for any n 2 N, there exists a set of n graphs with O(n) vertices having equal oriented incidence energy.