关于C_m×P_k的反强迫数

On the Anti-Forcing Number of C_m×P_k

摘要: 设G 是一个有完美匹配的简单连通图。若G 的一个边子集S 满足G-S 只有唯一完美匹配，则称S 是G 的一个反强迫集。G 中最小的反强迫集的大小称为G 的反强迫数。本文主要研究圈和路的卡什积图的反强迫数。根据一个图有唯一完美匹配的必要条件，我们证明了C₃×P_2k，C_2K+1×P₂，C₄×P 的反强迫数都为_k+1，并表明了C_2k×P₂ (k≥2) 的反强迫数恒为3。

Abstract: Let G be a simple connected graph with a perfect matching, S an edge set of G. We call S an anti- forcing set of G, if G-S contains only one perfect matching of G. The cardinality of the minimum anti-forcing set of G is called the anti-forcing number of G. In this paper, we study the anti-forcing number of the Cartesian product of a cycle and a path. According to the necessity of a graph with only one perfect matching, we show that the anti-forcing numbers of C₃×P_2k，C_2K+1×P₂，C₄×P are all _k+1 , and the anti-forcing number of C_2k×P₂ (k≥2) is 3.