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Distance-transitive graphs of valency five

Published online by Cambridge University Press:  20 January 2009

A. Gardiner  and
Cheryl E. Praeger
A. Gardiner
Affiliation:
Department of Mathematics, university of Birmingham, Birmingham B15 2TT, U.K.
Cheryl E. Praeger
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia
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If u and v are vertices of the (finite, connected) graph Γ, let d(u, v) denote the length of the shortest path joining u to v in Γ. The graph Γ is said to be distance-transitive if whenever d(u, v) = d(u′, v′), there exists an automorphism g of Γ such that ug = u′ and if vg = v′. Distance-transitive graphs of valency 3 and 4 were originally classified [2, 11, 12, 13] by using a computer to generate all “feasible intersection arrays” (cf. [1, Chapter 20]). In both cases a classification has since been given by hand [4, 5]. Wecontinue this latter tradition and prove the following theorem—which was recently proved independently by Ivanov et al. using a computer [10].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 1 , February 1987 , pp. 73 - 81
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

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