An Upper Bound on the Diameter of a 3-Edge-Connected C4-Free Graph

Blessings T. Fundikwa (), Jaya P. Mazorodze () and Simon Mukwembi ()
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Blessings T. Fundikwa: University of Zimbabwe
Jaya P. Mazorodze: University of Zimbabwe
Simon Mukwembi: University of Zimbabwe

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1931-1938

Abstract: Abstract We give an upper bound on the diameter of a 3-edge-connected C4-free graph in terms of order. In particular we show that if G is a 3-edge-connected C4 free graph of order n, and diameter d, then the inequality $$d \le {{3n} \over 7} — {3 \over 7}$$ d ≤ 3 n 7 − 3 7 holds. Moreover, graphs are constructed to show that the bound is almost asymptotically sharp.

Keywords: Diameter; edge-connectivity; 05C12 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0505-6

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