A new vertex-distinguishing edge coloring algorithm based on objective function

A new algorithm for vertex-distinguishing edge coloring of graph is designed. First of all, by definition of vertex-distinguishing edge coloring, we know that there exist two constraints rules, one is the edge constraint and the other is the vertex color set constraint. Second, we established objective function according to the two constraint rules. Third, based on the exchange rules, an algorithm is designed to make the objective function meet the requirements. The algorithm steps are described in detail. The experimental results show that the vertex-distinguishing edge coloring obtained by the algorithm conforms to the coloring conditions. This algorithm can effectively solve this coloring problem of graphs with large number of vertices.