Enumeration of permanental sums of lattice graphs

摘要

The permanental sum PS(G) is the coefficients sum of the permanental polynomial of a graph G. In this work, we exhibit the explicit expressions of the permanental sums of quadrilateral linear chains on the plane and quadrilateral linear rings on the cylinder by establishing orientation graphs, respectively. Meanwhile, we show that the permanental sum of the hexagonal linear chain with n hexagons is (n+1)2, which determines the value of permanental sum of the extremal hexagonal chain in [9].