2015/03/06 by Qin Yang, Heping Zhang, Yang, Qin +3 · 1 citation
Chemistry · Mathematics · #05C70 #92E10 #Combinatorics (math.CO) #FOS: Mathematics #Fullerene Chemistry and Applications #Graph theory and applications #Synthesis and Properties of Aromatic Compounds #math.CO #msc:05C70 #msc:92E10
paper · pdf · doi:10.48550/arxiv.1503.01900
18 pages, 12 figures
arxiv created 2015/03/06 · openalex publication_date 2015/03/06 · arxiv updated 2015/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The anti-forcing number of a connected graph G is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching. In this paper, we show that the anti-forcing number of every fullerene has at least four. We give a procedure to construct all fullerenes whose anti-forcing numbers achieve the lower bound four. Furthermore, we show that, for every even n≥20 (n≠22,26), there exists a fullerene with n vertices that has the anti-forcing number four, and the fullerene with 26 vertices has the anti-forcing number five.