On the total distance between nodes in tournaments
In 1984, the reviewer gave a sharp upper bound for the sum \(g(T_n)\) of the distances between all ordered pairs of vertices in a strong tournament \(T_n\) of order \(n\) (see J. Graph Theory 8, 1-21 (1984; Zbl 0552.05048)). The result is strengthened by introducing the score \(s\) of some removable vertex \(v\) (i.e. \(T_n- v\) is strong): \(g(T_n)= \textstyle{{1\over 6}} (n+ 1) n(n- 1)+ 2n- 3- s(n- 1- s)\) and the extremal tournaments are characterized.
scientific article; zbMATH DE number 896539