The Characterizing Properties of (Signless) Laplacian Permanental Polynomials of Almost Complete Graphs

Abstract

Let G be a graph with n vertices, and let LG and QG denote the Laplacian matrix and signless Laplacian matrix, respectively. The Laplacian (respectively, signless Laplacian) permanental polynomial of G is defined as the permanent of the characteristic matrix of LG (respectively, QG). In this paper, we show that almost complete graphs are determined by their (signless) Laplacian permanental polynomials.