关键词: 子图同构, 母图同构, 对应点无限衍生技术

Abstract: How to determine the isomorphism of graphs is a difficult problem of graph theory，which is not completely solved so far.S.M.Ulam has proposed a conjecture concerning graphic isomorphism，named graph reconstruction.In this paper a new necessary and sufficient condition of graphic isomorphism is proved which is stated as following： two graphs are isomorphic if and only if their subgraphs are isomorphic and the new vertices as well as their adjancy edges are corresponding with the property of isomorphism.Based on the technique for unlimitedly generating the corresponding pairs of vertices，this condition is proved with the method of mathematical induction.

Key words: subgraphic isomorphism, graphic isomorphism, technique for unlimitedly generating the corresponding pairs of vertices