Bounding The Average Distance Of The Strong Orientations

The average distance of a graph (or directed graph) G, denoted byμ(G), isthe average among the distances between all pairs (ordered pairs) of vertices of G.If G is a 2-edge connected graph, then (?)_min(G) is the minimum average distanceμ(D) taken over all strong orientations D of G. In this paper, some lower andupper bounds to (?)_min(G) for 2-edge connected graphs, 2-edge connected graphswith cut vertices, joint graphs and Multipartite graphs are estabished in termsof the order, size, girth and optimal diameter of G. In particular, we show that1. Let |V(G)|=a, |V(H)|=b, a≤b, a+b=N and let b be written as the formb=k((?))+r,k∈{0,1,2,…}and r∈{0,1,2,…,((?))-1}.Then...