Laplacian of a Graph Covering and Its Applications

Abstract

Let G be a finite graph and \(\overline{G}\) be any graph covering over G. By applying the representation theory of symmetric groups, the Laplacian characteristic polynomial and the normalized Laplacian characteristic polynomial of \(\overline{G}\) are investigated. As applications, adopting the algebra method the Kirchhoff index, the multiplicative degree-Kirchhoff index and the complexity of any connected covering over a connected graph are derived.