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Sharp Bounds on the Diameter of a Graph

Published online by Cambridge University Press:  20 November 2018

W. F. Smyth
W. F. Smyth*
Affiliation:
Department of Computer Science & Systems Mcmaster University Hamilton, Ontario, Canada, L8S 4K1
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Abstract

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Let Dn.m, be the diameter of a connected undirected graph on n ≥2 vertices and n - 1 ≤ m ≤ s(n) edges, where s(n) = n(n — l)/2. Then Dn.s(n) = 1, and for ms(n) it is shown that

The bounds on Dn.m, are sharp.

Keywords

Primary 05C35Secondary 68R10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 1 , 01 March 1987 , pp. 72 - 74
Copyright
Copyright © Canadian Mathematical Society 01

References

1. Béla, Bollobás, diameter of random graphs, Trans. AMS 267-1 (1981) 41–52.Google Scholar
2. Chung, F.R.K. and Garey, M.R., Diameter bounds for altered graphs, J. Graph Theory 8 (1984) 511–534.Google Scholar
3. Bernard, Ghigny, Critique de l'algorithme de Smyth et Benzi, Master's thesis, Université Catholique de Lou vain (1984).Google Scholar
4. Victor, Klee and David, Larman, Diameters of random graphs, Can. J. Math. 33-3 (1981) 618–640.Google Scholar
5. Smyth, W.F., Algorithms for the reduction of matrix bandwidth and profile, J. Computational Appl. Math. 12 & 13 (1985) 551–561.Google Scholar
6. Smyth, W.F., Sparse random graphs have small diameter, Proc. 4th Hungarian Comp. Sci. Conf. (1985), to appear.Google Scholar