Some Extremal Graphs with Respect to Permanental Sum

Let G be a graph and A(G) the adjacency matrix of G. The polynomial π(G, x) = per (xI- A(G)) is called the permanental polynomial of G, and the permanental sum of G is the summation of the absolute values of the coefficients of π(G, x). In this paper, we give some upper and lower bounds for the permanental sum among spiro hexagonal chains, and the corresponding extremal graphs are determined. Furthermore, we investigate the more general result about permanental sum. We obtain a lower bound for the permanental sum of bipartite graphs and the corresponding extremal graphs are also determined.