Extremal values for ratios of distances in trees Original Research Article

The distance of a vertex u in a connected graph G is defined by σ(u) = ∑ v ϵ V(G)d(u, v) and the distance of G is given by σ(G) = 12 ∑ u ϵ V(G)σ(u). Extremal values for the ratios σ(T)σ(v), σ(T)σ(w), σ(w)σ(v), and σ(w)σ(u) are determined where T is a tree of order n, v is a centroid vertex of T, and w and u are end vertices of T.