Skip to main content Accesibility Help
×
×
Home

The groups of the generalized Petersen graphs

  • Roberto Frucht (a1), Jack E. Graver (a2) and Mark E. Watkins (a2)
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.).)

Copyright
References
Hide All
(1)Carmichael, R. D.Introduction to the theory of groups of finite order (Ginn, Boston, 1937).
(2)Coxeter, H. S. M.Self-dual configurations and regular graphs. Bull. Amer. Math. Soc. 56 (1950), 413455.
(3)Coxeter, H. S. M. and Moser, W. O. J.Generators and relations for discrete groups, Springer's Ergeb. N.F. 14 (Berlin, 1965).
(4)Foster, Ronald M.Census of trivalent symmetrical graphs, I, presented at the Second Waterloo Combinational Conference,University of Waterloo,Waterloo, Ontario, in April, 1966.
(5)Frucht, Roberto.Die gruppe des Petersen'schen Graphen und der Kantensysteme der regulären Polyeder. Comment. Math. Helv. 9, (1936/1937), 217223.
(6)Tutte, W. T.A family of cubical graphs. Proc. Cambridge Philos. Soc. 43 (1947), 459474.
(7)Tutte, W. T.Connectivity in graphs (University of Toronto Press, Toronto, 1966).
(8)Watkins, Mark E.A Theorem on Tait colorings with an application to the generalized Petersen graphs. J. Combinational Theory 6 (1969), 152164.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed