图的边重构性的一个注记

如果图Ｇ的每个边重构图都与图Ｇ同构，则称图Ｇ是边可重构的，图的边重构猜想是指所有的至少有４条边的有限无向简单图都是边可重构的，它是至今尚未解决的著名的图论问题之一，文章主要通过定义特殊函数的方法来研究图的边重构性问题，并给出仅以图的最大顶点次数和最小顶点次数作为参数的简单充分条件。

A note on edge reconstructions of graphs

A graph G is edge reconstructible if every edge reconstruction of graph G is isomorphic to graph G. The edge reconstruction conjecture of graphs means that all finite undirected simple graphs on at least four edges are edge reconstructible, one of the well known graph theory problems which remain to be solved so far. This paper mainly studies the edge reconstruction problems of graphs by using the method of defining special functions and presents two simple formal sufficient conditions only with the maximum degree and minimum degree of graphs as parameters.