Affiliation:
1. Department of Mathematics University of Zimbabwe P.O. Box MP167, Mount Pleasant Harare ZIMBABWE
2. School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal Westville Campus P Bag XG54001, Durban SOUTH AFRICA
Abstract
Abstract
We give asymptotically sharp upper bounds on the radius and diameter of
(i) a connected graph,
(ii) a connected triangle-free graph,
(iii) a connected C4-free graph of given order, minimum degree, and maximum degree.
We also give better bounds on the radius and diameter for triangle-free graphs with a given order, minimum degree and a given number of distinct terms in the degree sequence of the graph. Our results improve on old classical theorems by Erd˝os, Pach, Pollack and Tuza [Radius, diameter, and minimum degree, J. Combin. Theory Ser. B 47 (1989), 73-79] on radius, diameter and minimum degree.
Cited by
3 articles.
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1. Bounds on the Steiner radius of a graph;Discrete Mathematics, Algorithms and Applications;2022-10-04
2. Radius, girth and minimum degree;Journal of Graph Theory;2022-01-09
3. An Upper Bound on the Diameter of a 3-Edge-Connected C4-Free Graph;Indian Journal of Pure and Applied Mathematics;2020-12