PreprintCC BY 4.0arXiv
Average eccentricity in k-connected tournaments
Abstract
The average eccentricity avec(D) of a strong digraph D is the mean eccentricity of all vertices in D. A tournament T is an orientation of a complete graph. In this paper, we prove that the average eccentricity satisfies 2 ≤ avec(T) < n/2k + 11/2 + k/8n for a k-connected tournament T of order n. We further examine the case for strong tournaments where k = 1, and show that avec(T) ≤ (n+11)/2 + 1/8n for any strong tournament T. Moreover, we show that the lower bound $2$ is sharp and that the upper bounds are best possible apart from an additive constant.
Related
BibTeX
@misc{osaye2026average,
title = {{Average eccentricity in k-connected tournaments}},
author = {Fadekemi Janet Osaye},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35970},
eprint = {2610.35970},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35970},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Average eccentricity in k-connected tournaments
AU - Fadekemi Janet Osaye
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35970
UR - https://arxiv.org/abs/2610.35970
AB - The average eccentricity avec(D) of a strong digraph D is the mean eccentricity of all vertices in D. A tournament T is an orientation of a complete graph. In this paper, we prove that the average eccentricity satisfies 2 ≤ avec(T) < n/2k + 11/2 + k/8n for a k-connected tournament T of order n. We further examine the case for strong tournaments where k = 1, and show that avec(T) ≤ (n+11)/2 + 1/8n for any strong tournament T. Moreover, we show that the lower bound $2$ is sharp and that the upper bounds are best possible apart from an additive constant.
ER -