Characteristic Polynomials of Oriented Graphs

Abstract

Graph energy is defined as the sum of the absolute values of all eigenvalues and it has important applications related to molecular graphs. Directed graphs play important role in some applications in social sciences and network studies. There are some studies on several aspects related to directed graphs. But there is a special class of directed graphs called oriented graphs for which there is hardly nothing done. In this paper, we study the spectral properties of oriented graphs. We determine characteristic polynomials of several graph classes, we determine the effect of edge addition to characteristic polynomial. We show that the orientation of pendant edges is not important, but the orientation of the edges on a cycle effects the characteristic polynomial which shows difference from the classical graphs.