In this paper, we determine all connected 5-arc transitive cubic Cayley graphs on the alternating group A47; there are only two such graphs (up to isomorphism). By earlier work of the authors, these are the only two nonnormal connected cubic arc-transitive Cayley graphs for finite nonbelian simple groups, and so this paper completes the classification of such non-normal Cayley graphs.
A Cayley graph Γ = Cay(G, S) is called normal for G, if GR, the right regular representation of G, is a normal subgroup of the full automorphism group Aut(Γ ) of Γ . In this paper we determine the normality of connected and undirected Cayley graphs of valency three for dihedral g
A k-L(2, 1)-labelling of a graph G is a mapping f : V (G) → {0, 1, 2, . . . , k} such that |f(u)− f(v)| ≥ 2 if uv ∈ E(G) and f(u) 6= f(v) if u, v are distance two apart. The smallest positive integer k such that G admits a k-L(2, 1)-labelling is called the λ-number of G. In this
We prove that the underlying graphs of p-gonal r-valent orientably regular maps are arc-transitive but non-Cayley if r 3 and p is a prime greater than r(r ? 1).
We prove that the underlying graphs of p-gonal r-valent orientably regular maps are arc-transitive but non-Cayley if r ≥ 3 and p is a prime greater than r(r − 1).