An interesting fact is that almost all the connected 2-arc-transitive nonnormal Cayley graphs on nonabelian simple groups with small valency or prime (provided solvable vertex stabilizers) are alternating An. This naturally motivates study of for arbitrary valency. In this paper, we characterize automorphism such graphs. particular, show a non-complete (G,2)-arc-transitive graph G simple, socle...

Weakly s-arc transitive graphs are introduced and determined. A graph is said to be weakly s-arc transitive if its endomorphism monoid acts transitively on the set of s-arcs. The main results are: (1) A nonbipartite graph is weakly s-arc transitive if and only if it is s-arc transitive. (2) A tree with diameter d is weakly s-arc transitive for all 0 s d. (3) A bipartite graph with girth g = 2s ...

I describe a 27-vertex graph that is vertex-transitive and edgetransitive but not 1-transitive. Thus while all vertices and edges of this graph are similar, there are no edge-reversing automorphisms. A graph (undirected, without loops or multiple edges) is said to be vertextransitive if its automorphism group acts transitively on the set of vertices, edge-transitive if its automorphism group ac...

a graph $gamma$ is said to be vertex-transitive or edge‎- ‎transitive‎ ‎if the automorphism group of $gamma$ acts transitively on $v(gamma)$ or $e(gamma)$‎, ‎respectively‎. ‎let $gamma=cay(g,s)$ be a cayley graph on $g$ relative to $s$‎. ‎then, $gamma$ is said to be normal edge-transitive‎, ‎if $n_{aut(gamma)}(g)$ acts transitively on edges‎. ‎in this paper‎, ‎the eigenvalues of normal edge-tra...