A new algorithm for D(β)-vertices sum distinguishing edge coloring of graphs

Based on the graph generation algorithm, we propose a novel algorithm to solve the problem of D(β)-vertices sum 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 the following graphs; secondly, we input these matrices to our designed algorithm; thirdly, the algorithm will output the corresponding D(β)-vertices sum distinguishing edge coloring 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.