Reducible Edge Coloring of Points with Distance of 2 in some Associative Graphs

The edges of simple graph G(V, E) are mapped to the set of positive integers {1, 2 … k}, makes the color set of any two points with the same degree whose distance is not greater than positive integer 2 the same, which is called D(2) − Vertex Reducible Edge Coloring, or D(2) − VREC for short. In this paper, a new D(2) − VREC algorithm is designed based on the existing graph coloring concept. The algorithm uses iterative optimization method to solve all non-isomorphic graph sets within finite points. Through the analysis of experimental results, the coloring characteristics of several types of associative graphs are found, and some theorems are summarized and proved.