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On Moore graphs

Published online by Cambridge University Press:  24 October 2008

R. M. Damerell
R. M. Damerell
Affiliation:
Royal Holloway College, University of London
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Extract

In this paper, we shall first describe the theory of distance-regular graphs and then apply it to the classification of Moore graphs. The object of the paper is to prove that there are no Moore graphs (other than polygons) of diameter ≥ 3. An independent proof of this result has been given by Barmai and Ito(1). Taken with the result of (4), this shows that the only possible Moore graphs are the following:

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 2 , September 1973 , pp. 227 - 236
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Bannai, E. and Ito, T.On finite Moore graphs, to be published in J. Fac. Sci. Univ. Tokyo Sect. I.Google Scholar
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(3)Biggs, N. L. Finite groups of automorphisms. London Math. Soc. Lecture notes, no. 6 (1971).Google Scholar
(4)Hoffman, A. J. and Singleton, R. R.On Moore graphs with diameters 2 and 3. IBM J. Res. Develop. 4 (1960), 497–504.CrossRefGoogle Scholar
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(6)Singleton, R. R.There is no irregular Moore graph. Amer. Math. Monthly 75 (1968), 42–43.CrossRefGoogle Scholar