Pacific Journal of Mathematics

On graphical regular representations of cyclic extensions of groups.

Wilfried Imrich and Mark E. Watkins

Article information

Source
Pacific J. Math., Volume 55, Number 2 (1974), 461-477.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102910980

Mathematical Reviews number (MathSciNet)
MR0379268

Zentralblatt MATH identifier
0298.05128

Subjects
Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]

Citation

Imrich, Wilfried; Watkins, Mark E. On graphical regular representations of cyclic extensions of groups. Pacific J. Math. 55 (1974), no. 2, 461--477. https://projecteuclid.org/euclid.pjm/1102910980


Export citation

References

  • [1] C. Y. Chao, On a theorem of Sabidussi, Proc. Amer. Math. Soc, 15 (1964), 291- 292.
  • [2] H. S. M. Coxeter and W. 0. J. Moser, Generators and Relations forDiscrete Groups, Springer-Verlag, Berlin, 1965.
  • [3] Marshall Hall, Jr. and James K. Senior, The Groups of Order 2n (n ^ 6), Macmillan, New York, 1964.
  • [4] Wilfried Imrich, Graphs with transitiveAbelian automorphismgroup in Com- binatorialTheoryand Its Applications,Coll. Soc. Janos Bolyai 4, Balatonfred, Hungary, (1969), 651-656.
  • [5] Rudolf Kochendrffer, Lehrbuch der Gruppentheorieunter besonderer Berucksich- tigung der endlichen Gruppen, Leipzig, 1966.
  • [6] Lewis A. Nowitz, On the non-existence of graphs with transitivegeneralized dicyclic groups, J. Combinatorial Theory, 4 (1968), 49-51.
  • [7] Lewis A. Nowitz and Mark E. Watkins, Graphicalregular representationsof non-abelian, groups I, Canad. J. Math., 24 (1972), 993-1008.
  • [8] Lewis A. Nowitz and Mark E. Watkins, Graphical regular representationsof non-abelian groups, II, Canad. J. Math., 24 (1972), 1009-1018.
  • [9] Gert Sabidussi, On a class of fixed-point free graphs, Proc. Amer. Math. Soc, 9 (1958), 800-804.
  • [10] Gert Sabidussi, On vertex-transitivegraphs, Monatsh. Math., 68 (1964), 426-438.
  • [11] Mark E. Watkins, On the action of non-abelian groups on graphs, J. Combinatorial Theory, 11 (1971), 95-104.
  • [12] Mark E. Watkins, Graphical regular representationsof alternating, symmetric, and mis- cellaneous small groups, Aequat. Math. 11 (1974), 40-50.
  • [13] Mark E. Watkins and Lewis A. Nowitz, On graphical regular representations of direct products of groups, Monatsh. Math., 76 (1972), 168-171.