图的点可区别边染色猜想的算法

Algorithm for Conjecture of Vertex Distinguishing Edge Coloring of Graphs

针对图K_(2n)\E(k_1,m)的点可区别边色数猜想,设计了一种新型的点可区别边染色算法.根据点可区别边染色的约束条件构建目标函数,利用交换规则进行逐步寻优,直到目标函数的值满足要求时染色成功.同时给出了算法的执行步骤、分析和测试结果.实验结果表明,该算法验证了猜想是成立的.

A proper edge coloring of a graph such that no two vertices have the same color set is called vertex distinguishing edge coloring,and the minimal number of coloring is called vertex distinguishing edge chromatic number.A new algorithm of vertex distinguishing edge coloring has been designed for conjecture of K（2n）／E（k1,m）.Accurately,the algorithm has established objective function by the constraint rules of vertex distinguishing edge coloring,used exchange rules to optimize the results gradually and accomplished coloring till the value of objective function met the requirements.And also described the algorithm steps,algorithm analysis and test results.The experimental results show that the conjecture is right.