Research On Edge Average Wiener Index Of Some Graphs

Abstract:Let G=(V, E) be a simple connected graph with vertex set V and edge set E. Wiener index W(G) of G is the sum of distances all pairs of vertices in G,i.e, where dG (u,v) is the distance between vertices u and v in G.For two edges f=uv and g=xy of a connected graph G, DG(f,g) is called the average distance of f and g, where DG(f,g) is called edge average Wiener index We’(G) of G.In this paper, we firstly give the research background of edge average Wiener index and basic definitions. Secondly, we introduce edge average Wiener index of fan graph, wheel graph, double fan graph, complete bipartite graph, middle graph of path, and an edge average Wiener index formula of tree. Finally, we mainly in-troduce relationship between We’(G) and W(L(G)), and relationship between We’(G) and W(G)...