The D-weight of a graph

Let G = (V(G), E(G)) be finite, undirected graph containing no loops nor multiple edges, with vertex set V(G) and edge set E(G). The index of an edge e in G is the number of neighboring edges of e while the V-weight of G, denoted by w(G), is the total of the indices of edges present E(G). The rational weight of G as defined by Guerrero, Guerrero and Artes in [2] is the sum of the degree vertices in G divided by the order of G. This paper investigates the properties of the graph parameter w(G) and illustrates this concept to some special classes of graphs, namely: paths, cycles, fans, wheel graphs, bipartite graphs and complete graphs. In addition, this paper studies the relationship of w(G) to the D-weight and rational weight of the line graph of G