Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Graphs associated with a group

Author: R. J. Plemmons
Journal: Proc. Amer. Math. Soc. 25 (1970), 273-275
MSC: Primary 05.62
MathSciNet review: 0263705
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that every group is isomorphic to a maximal group of graphs under the operation of graph product. In addition, maximal groups associated with an order graph are investigated.

References [Enhancements On Off] (What's this?)

  • [1] C. C. Chang and A. Ehrenfeucht, A characterization of abelian groups of automorphisms of a simply ordering relation, Fund. Math. 51 (1962/63), 141-147. MR 26 #198. MR 0142629 (26:198)
  • [2] P. M. Cohn, Groups of order automorphisms of ordered sets, Mathematika 4 (1957), 41-50. MR 19, 940. MR 0091280 (19:940e)
  • [3] R. Frucht, On the construction of partially ordered systems with a given group of automorphisms, Rev. Un. Mat. Argentina 13 (1948), 12-18. MR 9, 409. MR 0023821 (9:409c)
  • [4] C. Goffman, The group of similarity transforms of a simply ordered set, Bull. Amer. Math. Soc. 60 (1954), 289.
  • [5] R. L. Hemminger, On the group of a directed graph, Canad. J. Math. 18 (1966), 211-220. MR 32 #2346. MR 0184875 (32:2346)
  • [6] O. Ore, Theory of graphs, Amer. Math. Soc. Colloq. Publ., vol. 38, Amer. Math. Soc., Providence, R. I., 1962. MR 27 #740. MR 0150753 (27:740)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05.62

Retrieve articles in all journals with MSC: 05.62

Additional Information

Keywords: Automorphism group, directed graph, graph product, idempotent graph, maximal group of graphs, partial order graph, reduced graph
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society