Matching forcing polynomial of generalized Petersen graph GP(n, 2)

Abstract

Harary et al. and Klein and Randić proposed the forcing number of a perfect matching in mathematics and chemistry, respectively. In detail, the forcing number of a perfect matching M of a graph G is the smallest cardinality of subsets of M that are contained in no other perfect matchings of G. The author and cooperators defined the forcing polynomial of G as the count polynomial for perfect matchings with the same forcing number of G, from which the average forcing number, forcing spectrum, and the maximum and minimum forcing numbers of G can be obtained. Up to now, a few papers have been considered on matching forcing problem of nonplane non-bipartite graphs. In this paper, we investigate the forcing polynomials of generalized Petersen graphs GP (n, 2) for n = 5, 6, . . . , 15, which is a typical class of non-plane non-bipartite graph.