Further results on the permanental sums of bicyclic graphs

2023/11/23 by Wu, Tingzeng, Bai, Yinggang
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.13943

Abstract

Let G be a graph, and let A(G) be the adjacency matrix of G. The permanental polynomial of G is defined as π(G,x)=per(xI-A(G)). The permanental sum of G can be defined as the sum of absolute value of coefficients of π(G,x). Computing the permanental sum is #P-complete. Any a bicyclic graph can be generated from three types of induced subgraphs. In this paper, we determine the upper bound of permanental sums of bicyclic graphs generated from each a type of induced subgraph. And we also determine the second maximal permanental sum of all bicyclic graphs.

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