Vertex Magic Reducible Edge Labeling Algorithm for graphs

There exists a mapping f: E (g)→{1,2, …, Q}, for an undirected connected graph G (p, q), where p is the number of vertices and q is the number of edges, the associated edges of those vertices with the same degree in the graph have the same labeling sum. This f is denoted as Vertex Magic Reducible Edge Labeling(VMREL). In this paper, based on the research of edge-magic labeling and reducible coloring, the concept of Vertex Magic Reducible Edge Labeling is proposed, Vertex Magic Reducible Edge Labeling Algorithm is designed. The graph labeling results which satisfy all vertices with the same degree and the maximum labeling number of the associated edges is the total number of edges in the graph are filtered by iterative adjustment. In this paper, more than 10 million labeling results of graphs within 10 vertices were obtained by using Vertex Magic Reducible Edge Labeling Algorithm. Through analyzing the topological structure and labeling law of results, some theorems are summarized and proved.