冠图Kn�Km 的两种边度结合重构数

摘要

图的重构猜想是 Ulam和Kelly在20世纪中叶提出的一个著名的难题,之后,Harary提出边重构猜想,它是指任何一个至少含有4条边的图能够被它的边主子图集所唯一确定,通过分析冠图Kn�Km 的一个边主子图可能重构的图的结构,从而确定了它的两种边度结合重构数,进一步丰富了结构图论的内容。%The Reconstruction Conjecture of Ulam and Kelly has been open for more than 50 years.Then,Harary pro-posed Edge-Reconstruction Conj ecture,it states that every graph with more than three edges is determined by its edge-card.Two kinds of degree associated edge reconstruction numbers of the graph Kn�Km are determined by considering the possible reconstructions from a degree-associate edge-card.The results enrich the structure property of graphs.