求解图同构的判定算法

摘要

图同构的判定性问题是图论理论中的一个难题,至今没有得到彻底解决.受Ulam猜想的启发,提出了一个新的判定图同构的充分必要条件:在子图同构的前提下,根据新增顶点及相应关联边的关系,利用子图同构函数,判断父图同构的充分必要条件.基于具有同构关系的对应点无限衍生技术,采用反证法证明了这个充分必要条件的成立.设计并实现了图同构的一个判定算法,通过实例验证了算法的正确性和有效性.%How to determine the isomorphism of graphs is a difficult problem of graph theory,which has not been completely solved so far.From the idea of Ulam conjecture concerning graph isomorphism,a new necessary and sufficient condition of graph isomorphism is presented, 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 adjacency edges are corresponding.With the help of the technique for unlimitedly generating the corresponding pairs of vertices, this condition is proved with the method of reduction to absurdity.An algorithm for determining graph isomorphism is designed and implemented, whose correctness and validity are tested and verified with some concrete examples.