An Upper Bound on the Radius of a 3-Vertex-Connected C 4 -Free Graph

We show that if G is a 3-vertex-connected C 4 -free graph of order n and radius r , then the inequality r ≤ 2 n / 9 + O 1 holds. Moreover, graphs are constructed to show that the bounds are asymptotically sharp.

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2020-08, Vol.2020, p.1-7
Main Authors: Fundikwa, Blessings T., Mazorodze, Jaya P., Mukwembi, Simon
Format: Article
Language:English
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Description
Summary:We show that if G is a 3-vertex-connected C 4 -free graph of order n and radius r , then the inequality r ≤ 2 n / 9 + O 1 holds. Moreover, graphs are constructed to show that the bounds are asymptotically sharp.
ISSN:2314-4629
2314-4785
DOI:10.1155/2020/8367408