Electronic Resource
Springer
Journal of algebraic combinatorics
1 (1992), S. 275-282
ISSN:
1572-9192
Keywords:
half-transitive graphs
;
Cayley graphs
;
simple groups
;
Schur multiplier
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We call an undirected graph X half-transitive if the automorphism group Aut X of X acts transitively on the vertex set and edge set but not on the set of ordered pairs of adjacent vertices of X. In this paper we determine all half-transitive graphs of order p 3 and degree 4, where p is an odd prime; namely, we prove that all such graphs are Cayley graphs on the non-Abelian group of order p 3 and exponent p 2, and up to isomorphism there are exactly (p − 1)/2 such graphs. As a byproduct, this proves the uniqueness of Holt's half-transitive graph with 27 vertices.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1022440002282
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