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

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

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Let G be a graph with n vertices, and let LG and SD Cards QG denote the Laplacian matrix and signless Laplacian matrix, respectively.The Laplacian (respectively, signless Laplacian) permanental polynomial of G is defined as the face scrub 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.