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A Construction for Vertex-Transitive Graphs

Published online by Cambridge University Press:  20 November 2018

Brian Alspach  and
T. D. Parsons
Brian Alspach
Affiliation:
Simon Fraser University, Burnaby, British Columbia
T. D. Parsons
Affiliation:
Pennsylvania State University, University Park, Pennsylvania
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A useful general strategy for the construction of interesting families of vertex-transitive graphs is to begin with some family of transitive permutation groups and to construct for each group Γ in the family all graphs G whose vertex–set is the orbit V of Γ and for which Γ ≦ Aut (G), where Aut (G) denotes the automorphism group of G. For example, if we consider the family of cyclic groups 〈(0 1 … n – 1)〉 generated by cycles (0, 1 … n – 1) of length n, then the corresponding graphs are the n-vertex circulant graphs.

In this paper we consider transitive permutation groups of degree mn generated by a “rotation” ρ which is a product of m disjoint cycles of length n and by a “twisted translation” t; such that τρτ–l = ρα for some α.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 2 , 01 April 1982 , pp. 307 - 318
Copyright
Copyright © Canadian Mathematical Society 1982

References

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