二部克莱茵瓶六角系统K(p,q,t)的强迫数I.p≤q或q<p≤2q

The Forcing Number of Bipartite Klein Bottle Polyhexs I.p≤q or q < p≤2q

能惟一确定图G的完美匹配M的最小不交边子集所含的边数称作完美匹配M的强迫数.完美匹配强迫数在有机化学上也称作凯库勒结构的原始自由度,来源于对分子共振结构的研究,是化学分子图的一个重要拓扑不变量.给出了二部克莱茵瓶六角系统K(p,q,t)的强迫数下界,并表明当p≤q时,K(p,q,t)的最小强迫数为p;若q<p≤2q,K(p,q,t)的最小强迫数为q.

The forcing number of a perfect matching M of a graph G is the cardinality of the smallest subset of M that is contained in no other perfect matching of G. The same idea appeared in earlier papers by Randid and Klein in terms of ＂innate degree of freedom＂ of a Kekule structure. In this paper, we consider the forcing number of a bipartite Klein bottle polyhex K（p, q, t） with a torsion t, a cubic graph embedded on Klein bottle with every face being a hexagon. We obtain that f（K（p, q, t）） 〉1 min{p, q}, and if p≤ q, then f（K（p, q, t）） = p; else if q 〈 p ≤ 2q, then f（K（p, q, t）） = q.