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On the oriented incidence energy and decomposable graphs

Stevanović Dragan (Faculty of Science and Mathematics, Niš)
de Abreu Nair M.M. (Fluminense Federal University, Mathematical Institute, Praça do Valonguinho, Centro, Niterói, Brazil)
de Freitas Maria A.A. (Fluminense Federal University, Mathematical Institute, Praça do Valonguinho, Centro, Niterói, Brazil)
Vinagre Cybele
Del-Vecchio Renata

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.

Keywords: Laplacian-like energy, incidence energy, Decomposable graphs