图的边重构性

Edge reconstruction of graph

提出图的小次、大次和特殊路长S(G)等概念来研究图的边重构性,并得到如下两个重要结论:若图G存在次为δ_p+k的顶点至少和k+1个小次顶点相邻,则G是边可重构的(δ_p为某小次,k为非负整数);若S(G)≠0,3,+∞,则G是边可重构的。

The definition of small degree and large degree is given, and it is used to study the edge reconstructions of graphs, and two results are obtained. Firstly, let G be a graph of small degree δ_1<δ_2<…<δ_m, if for some k≥0, there is a vertex in G of degree δ_i+k adjacent to. k+1 or more vertice of small degree, then G is edge reconstructible. Secondly,let s (G) be the length of a special path in G, if S (G)(?)0, 3,+4-co, then G is edge reconstructible.