5-Arc transitive cubic Cayley graphs on finite simple groups

Cubic s-arc transitive Cayley graphs

“…Theorem 1.2 is a direct consequence of Corollary 2.2 and Theorem 1.1. Finally, since a Cayley graph of a finite non-abelian simple group is either normal or core-free, our argument leads to the following well-known result which can be derived from [15,27,28]. Theorem 4.1.…”

“…Then Cos(X , H, τ ) ∼ = Cay(G, S) is a connected core-free X -edge-transitive Cayley graph with respect to G, where X = τ , H , G = {σ ∈ X |1 σ = 1} and S = {σ ∈ Hτ H|1 σ = 1}. Note that all isomorphic regular subgroups of S n are conjugate in S n (see [28], for example). Thus, up to isomorphism, Cos(X , H, τ ) is independent of the choice of H. Note that Cos(X , H, τ ) ∼ = Cos(X σ , H, τ σ ) for any σ ∈ N S n (H).…”

Connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups

“…The first lemma comes from the literature [12]. (2) Γ is normal for G if S consists of three involutions.…”

“…On the other hand, we know from [11,12] that for almost finite nonabelian simple groups, except only the alternating group A 47 , their connected cubic s-arc-transitive Cayley graphs are normal and hence s 2. It follows that these graphs are either 1-or 2-arc-transitive.…”

Cubic arc-transitive Cayley graphs on Frobenius groups

“…In particular, there are many results about cubic Cayley graphs. For instance, see [11,16,17] for cubic symmetric Cayley graphs on finite nonabelian simple groups, which are normal except for A 47 , see [12] for a characterization of connected cubic s-transitive Cayley graphs, and see [5] for a classification of the connected arc-transitive cubic Cayley graphs on PSL(2, p) where p ≥ 5 is a prime. The objective of this paper is to give a characterization of cubic arc-transitive Cayley graphs on a class of Frobenius groups.…”