A new algorithm for obtaining the vertex distinguishing edge coloring of graphs

We design a new algorithm, based on the graph generation method, to solve the problem of vertex distinguishing edge coloring of some kinds of special graphs. Our main contributions to solving this graph coloring problem are: firstly, we generate the adjacent matrices of graphs; secondly, we input these matrices to our proposed algorithm; thirdly, the algorithm will output the corresponding vertex distinguishing edge colored matrices; fourthly, through analyzing of the results obtained by our algorithm, we conclude that regular chromatic number are found in some of the graphs involved. We think that our proposed algorithm is innovative and can be adopted by other researchers.