Oriented Incidence Energy and Threshold Graphs

Dragan Stevanović

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 $n\geq9$, there exists at least $(\frac{[n/9]}2)+1$ distinct pairs of graphs on $n$ vertices having equal oriented incidence energy.