Graphs with Extremal Incidence Energy

Abstract

For a simple connected graph $G$, the incidence energy $IE(G)$ is defined as the sum of all singular values of its incidence matrix. In this paper, we characterize the graphs with the maximum incidence energies among all graphs with given chromatic number and given pendent vertex number, respectively. We also characterize the graphs with the minimum incidence energy among all graphs with given clique number. Especially, we characterize the tree with the minimum incidence energy among all trees with given pendent vertex number.