A note on the triameter of graphs
Combinatorics
2025-07-29 v1
Abstract
In this note, we give answers to three questions from the paper [A. Das, Triameter of graphs, Discuss. Math. Graph Theory, 41 (2021), 601--616]. Namely, we obtain a tight lower bound for the triameter of trees in terms of order and number of leaves. We show that in a connected block graph any triametral triple of vertices contains a diametral pair and that any diametral pair of vertices can be extended to a triametral triple. We also present several open problems concerning the interplay between triametral triples, diametral pairs and peripheral vertices in median and distance-hereditary graphs.
Keywords
Cite
@article{arxiv.2103.10806,
title = {A note on the triameter of graphs},
author = {Artem Hak and Sergiy Kozerenko and Bogdana Oliynyk},
journal= {arXiv preprint arXiv:2103.10806},
year = {2025}
}