The algorithm for adjacent vertex distinguishing proper edge coloring of graphs

An adjacent vertex distinguishing proper edge coloring of a graph G is a proper edge coloring of G such that no pair of adjacent vertices meet the same set of colors. The minimum number of colors is called adjacent vertex distinguishing proper edge chromatic number of G. In this paper, we present a new heuristic intelligent algorithm to calculate the adjacent vertex distinguishing proper edge chromatic number of graphs. To be exact, the algorithm establishes two objective subfunctions and a main objective function to find its optimal solutions by the conditions of adjacent vertex distinguishing proper edge coloring. Moreover, we test and analyze its feasibility, and the test results show that this algorithm can rapidly and efficiently calculate the adjacent vertex distinguishing proper edge chromatic number of graphs with fixed order, and its time complexity is less than O(n(3)).