2017/07/12 by Shuang Zhao, Zhao, Shuang, Jinjiang Zhu +4
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #math.CO
paper · pdf · doi:10.48550/arxiv.1707.03701
arxiv created 2017/07/12 · openalex publication_date 2017/07/12 · arxiv updated 2017/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 forcing spectrum of G is the collection of forcing numbers of all perfect matchings of G. In this paper, we classify the perfect matchings of a generalized Petersen graph P(n,2) in two types, and show that the forcing spectrum is the union of two integer intervals. For n≥ 34, it is [\lceil \frac n 12 \rceil+1,\lceil \frac n+3 7 \rceil +δ(n)]∪ [\lceil \frac n+2 6 \rceil,\lceil \frac n 4 \rceil], where δ(n)=1 if n≡ 3 (mod 7), and δ(n)=0 otherwise.