Proximity and remoteness in directed and undirected graphs

Let D be a strongly connected digraph. The average distance σ̄(v) of vertex v is the arithmetic mean distances from to all other vertices D. remoteness ρ(D) and proximity π(D) are maximum minimum D, respectively. We obtain sharp upper lower bounds on as function order n describe extreme digraphs for bounds. also such strong tournaments. show that tournament T, we have π(T)=ρ(T) if only T regular. Due this result, one may conjecture every digraph with π(D)=ρ(D) present an infinite family non-regular π(D)=ρ(D). undirected graphs well.