具有唯一完美匹配的D-图

摘要

A new graph operator was introduced to aid in the investigation of Tutte sets and extreme sets of graphs which had perfect matchings in[1,2],and many interesting properties had been obtained.In this paper,we characterize the saturated graph G having unique perfect matching with level(G)=0 and give the sharp upper bound of the number of lines of the D-graph D(G) of the graphs with unique perfect matching.%为了研究具有完美匹配图的Tutte集和极端集,文献[1,2]提出了一种新的图运算,并且得到了许多有趣的性质.本文中,我们刻画了level(G)=0的具有唯一完美匹配的饱和图G,并且确定了具有唯一完美匹配图的D-图的边数的紧上界.