2021/10/08 by Shuang Zhao, Zhao, Shuang
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2110.03978
openalex publication_date 2021/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.