The characterizing properties of (signless) Laplacian permanental polynomials of almost complete graphs (Q2052128)

Summary: Let \(G\) be a graph with \(n\) vertices, and let \(L(G)\) and \(Q(G)\) 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 \(L(G)\) (respectively, \(Q(G)\)). In this paper, we show that almost complete graphs are determined by their (signless) Laplacian permanental polynomials.