Graphs with Given Automorphism Group and Few Edge Orbits

László Babai, Albert J. Goodman, L. Lovász

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A graph X is said to represent the group G with k edge (vertex) orbits if the automorphism group of X is isomorphic to G and it acts with k orbits on the set of edges (vertices, resp.) of X. It is known that (with three exceptions) every finite group can be represented with ➯2 vertex orbits (Babai, 1974). In this paper we build a framework to study the minimum number of edge orbits. We show that surprisingly large classes of groups admit a representation with a bounded number of edge-orbits. These include the groups generated by a bounded number of abelian subgroups; in particular, any direct product of finite simple groups. The case of abelian groups is related to work of Brenner, and of Gelfand and Ponomarev.

Original languageEnglish
Pages (from-to)185-203
Number of pages19
JournalEuropean Journal of Combinatorics
Volume12
Issue number3
DOIs
Publication statusPublished - Jan 1 1991

Fingerprint

Automorphism Group
Orbit
Graph in graph theory
Finite Simple Group
Direct Product
Vertex of a graph
Exception
Abelian group
Finite Group
Isomorphic
Subgroup

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Graphs with Given Automorphism Group and Few Edge Orbits. / Babai, László; Goodman, Albert J.; Lovász, L.

In: European Journal of Combinatorics, Vol. 12, No. 3, 01.01.1991, p. 185-203.

Research output: Contribution to journalArticle

Babai, László ; Goodman, Albert J. ; Lovász, L. / Graphs with Given Automorphism Group and Few Edge Orbits. In: European Journal of Combinatorics. 1991 ; Vol. 12, No. 3. pp. 185-203.
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