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Harary et al. and Klein and Randic proposed the forcing number of a perfectmatching in mathematics and chemistry, respectively. In detail, the forcingnumber of a perfect matching M of a graph G is the smallest cardinality ofsubsets of M that are contained in no other perfect matchings of G. The authorand cooperators defined the forcing polynomial of G as the count polynomial forperfect matchings with the same forcing number of G, from which the averageforcing number, forcing spectrum, and the maximum and minimum forcing numbersof G can be obtained. Up to now, a few papers have been considered on matchingforcing problem of non-plane non-bipartite graphs. In this paper, weinvestigate the forcing polynomials of generalized Petersen graphs GP(n, 2) forn = 5, 6, . . . , 15, which is a typical class of non-plane non-bipartitegraph.

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