On the total distance between nodes in tournaments
type: Item
instance of: scholarly article
title: On the total distance between nodes in tournaments
zbMATH Open document ID: 0854.05041
DOI: 10.1016/0012-365X(94)00094-Y
published in: Discrete Mathematics
publication date: 1997-01-13T00:00:00Z
review text: 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.
reviewed by: Ján Plesník
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 896539
zbMATH Keywords: digraph
zbMATH Keywords: distances
zbMATH Keywords: tournament
author: J. W. Moon
MaRDI profile type: Publication
cites work: Q4100106
cites work: Q5585195
cites work: On the sum of all distances in a graph or digraph
cites work: Q3872493
cites work: Mean distance in a tree
full work available at URL: 0012-365x(94)00094-y
OpenAlex ID: W2071368728
description: scientific article; zbMATH DE number 896539