AVERAGE DEGREE LABELING OF GRAPHS

Let G be an undirected, simple, connected graph. If a graph G has vertices labeled by degrees and edges labeled by the least of the average of the degrees of their end vertices, then the graph is said to permit average-degree edge labeling. This paper discusses the average degree edge labeling of complete bipartite graphs, the join of the Path graph P_m and the Complete graph K_n, and of various classes of trees. Using the average degree labeling graph, we can determine the shortest path between the vertices. Additionally, we have tried to develop an algorithm for spanning trees of average degree labeled networks, both maximal and minimal.