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arXiv · 2103.10806

A note on the triameter of graphs

Artem Hak·Sergiy Kozerenko·Bogdana Oliynyk
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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.

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Artem Hak, Sergiy Kozerenko, Bogdana Oliynyk. 2021-03-19. A note on the triameter of graphs. https://doi.org/10.1016/j.dam.2021.12.011

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