Journal ArticleDOI
Tournaments with given regular group
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This article is published in Aequationes Mathematicae.The article was published on 1978-02-01. It has received 32 citations till now.read more
Citations
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Sidon Sets in Groups and Induced Subgraphs of Cayley Graphs
László Babai,Vera T. Sós +1 more
TL;DR: It is proved that most graphs on n vertices are not induced subgraphs of any vertex transitive graph with the help of Fourier analysis.
Journal ArticleDOI
Finite digraphs with given regular automorphism groups
TL;DR: With five exceptions, every finite regular permutation group occurs as the automorphism group of a digraph as discussed by the authors, with five exceptions being the permutation groups of the digraphs.
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On the Automorphism Groups of almost all Cayley Graphs
László Babai,Chris Godsil +1 more
TL;DR: This conjecture that, unless G belongs to a known class of exceptions, almost all Cayley graphs of G have G for their full automorphism group is proved for nilpotent groups of odd order.
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Infinite digraphs with given regular automorphism groups
TL;DR: It is proved that, given an infinite group G there is a directed graph X such that its automorphism group A(X) is the regular representation of G .
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Every finite non-solvable group admits an oriented regular representation
Joy Morris,Pablo Spiga +1 more
TL;DR: It is shown that every finite non-solvable group admits an ORR, and a tool is provided that may prove useful in showing that some families of finite solvable groups admit ORRs.
References
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Journal ArticleDOI
On a class of fixed-point-free graphs
TL;DR: In this paper, it was shown that for any two vertices x and y of X there is at most one 4GG(X) which sends x into y, which is precisely the fact which was used in [i] and [2] to prove that G(X), G(G) actually is isomorphic to G.
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On the action of non-Abelian groups on graphs
TL;DR: In this paper, it was shown that the class of finite groups having the above regular representations is closed under the operation of direct product, and that for finite groups of order p 3 for p an odd prime (except for one group of order 27).
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Graphical Regular Representations of Non-Abelian Groups, II
Lewis A. Nowitz,Mark E. Watkins +1 more
TL;DR: In this paper, it was shown that a given finite non-abelian group G has a graphical regular representation if (G|, 6) = 1 and an affirmative answer was given if G = 1.
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On automorphism groups of cayley graphs
W. Imrich,Mark E. Watkins +1 more
TL;DR: In this article, the authors considered the problem of minimizing the index of the Cayley graph of a finite group with respect to a subset of elements of the group, in particular when this index is always greater than 1.