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The groups of the generalized Petersen graphs

Published online by Cambridge University Press:  24 October 2008

Roberto Frucht ,
Jack E. Graver  and
Mark E. Watkins
Roberto Frucht
Affiliation:
Universidad Tecnica Santa Maria, Valparaiso, Chile
Jack E. Graver
Affiliation:
Syracuse University, Syracuse, New York 13210
Mark E. Watkins
Affiliation:
Syracuse University, Syracuse, New York 13210
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Extract

1. Introduction. For integers n and k with 2 ≤ 2k < n, the generalized Petersen graph G(n, k) has been defined in (8) to have vertex-set

and edge-set E(G(n, k)) to consist of all edges of the form

where i is an integer. All subscripts in this paper are to be read modulo n, where the particular value of n will be clear from the context. Thus G(n, k) is always a trivalent graph of order 2n, and G(5, 2) is the well known Petersen graph. (The subclass of these graphs with n and k relatively prime was first considered by Coxeter ((2), p. 417ff.).)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 2 , September 1971 , pp. 211 - 218
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

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