On cubic Cayley graphs of finite simple groups

Fang, Xin; Li, Cai Heng; Wang, Jie; Xu, Ming

doi:10.1016/s0012-365x(01)00075-9

Cited by 55 publications

(37 citation statements)

References 21 publications

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“…Wang et al [19] obtained all disconnected normal Cayley graphs. Let Cay(G, S) be a connected cubic Cayley graph on a non-abelian simple group G. Praeger [17] proved that if N Aut(Cay(G,S)) (R(G)) is transitive on edges then the Cayley graph Cay(G, S) is normal, and Fang et al [5] proved that the vast majority of connected cubic Cayley graphs on non-abelian simple groups are normal. Baik et al [2,3] listed all connected non-normal Cayley graphs on abelian groups with valency less than 6 and Feng et al [7] proved that all connected tetravalent Cayley graphs on p-groups of nilpotent class 2 with p an odd prime are normal.…”

Section: Introductionmentioning

confidence: 99%

Automorphism groups of Cayley graphs on symmetric groups with generating transposition sets

Feng

2006

Journal of Combinatorial Theory, Series B

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Let T be a set of transpositions of the symmetric group S n . The transposition graph Tra(T ) of T is the graph with vertex set {1, 2, . . . , n} and edge set {ij | (i j ) ∈ T }. In this paper it is shown that if n 3, then the automorphism group of the transposition graph Tra(T ) is isomorphic to Aut(S n , T ) = { ∈ Aut(S n ) | T = T } and if T is a minimal generating set of S n then the automorphism group of the Cayley graph Cay(S n , T ) is the semiproduct R(S n ) Aut(S n , T ), where R(S n ) is the right regular representation of S n . As a result, we generalize a theorem of Godsil and Royle [C.D. Godsil, G. Royle, Algebraic Graph Theory, Springer, New York, 2001, p. 53] regarding the automorphism groups of Cayley graphs on S n : if T is a minimal generating set of S n and the automorphism group of the transposition graph Tra(T ) is trivial then the automorphism group of the Cayley graph Cay(S n , T ) is isomorphic to S n .

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Section: Introductionmentioning

confidence: 99%

Automorphism groups of Cayley graphs on symmetric groups with generating transposition sets

Feng

2006

Journal of Combinatorial Theory, Series B

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“…Much structural information of is contained in the full automorphism group Aut , such as the degree of symmetry of , and the isomorphism class of among Cayley graphs of G (refer to [10]). Generally, Aut is larger thanĜ Aut(G, S), see for example [4,6,11,16]. Theorem 1.1 can be restated in the Cayley graph version.…”

Section: Some Related Problemsmentioning

confidence: 99%

“…Naturally, one would ask whether the condition in Conjecture 4.3 that Aut(G, S) is 2-transitive on S can be weakened to the condition that Aut(G, S) is only transitive on S, refer to [4,11,16,18].…”

Section: Some Related Problemsmentioning

confidence: 99%

On automorphism groups of quasiprimitive 2-arc transitive graphs

2007

J Algebr Comb

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“…If not, then A would have a faithful permutation representation of degree dividing 16, acting on the cosets of G R . Thus the order of a Sylow 3-subgroup of A is at most 3 6 . However, the order of a Sylow 3-subgroup of G is 3 3 f with f ≥ 3, a contradiction.…”

Section: Theorem 11 Let G Be a Finite Soluble Group And Be A (G 1)mentioning

confidence: 99%