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

TL;DR

This paper studies the forcing polynomial of perfect matchings in generalized Petersen graphs GP(n, 2), providing explicit calculations for n from 5 to 15, and contributing to the understanding of matching forcing problems in non-plane non-bipartite graphs.

Contribution

It introduces the forcing polynomial for generalized Petersen graphs GP(n, 2) and computes it explicitly for n=5 to 15, advancing the analysis of matching forcing in non-plane non-bipartite graphs.

Findings

Explicit forcing polynomials for GP(n, 2) with n=5 to 15.

Insights into the forcing spectrum and extremal forcing numbers.

Extension of matching forcing analysis to non-plane non-bipartite graphs.

Abstract

Harary et al. and Klein and Randic 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 non-plane 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.