‎darafsheh and assari in [normal edge-transitive cayley graphs on non-abelian groups of order 4p‎, ‎where $p$ is a prime number‎, ‎sci‎. ‎china math‎., ‎56 (1) (2013) 213-219.] classified the connected normal edge transitive and‎ ‎$frac{1}{2}-$arc-transitive cayley graph of groups of order $4p$‎. ‎in this paper we continue this work by classifying the‎ ‎connected cayley graph of groups of order...

darafsheh and assari in [normal edge-transitive cayley graphs onnon-abelian groups of order 4p, where p is a prime number, sci. china math. {bf 56} (1) (2013) 213$-$219.] classified the connected normal edge transitive and $frac{1}{2}-$arc-transitive cayley graph of groups of order$4p$. in this paper we continue this work by classifying theconnected cayley graph of groups of order $2pq$, $p > q...

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 ...

A construction is given of a valent arc transitive graph with vertex stabilizer isomorphic to the dihedral group D The graph has vertices and is the rst known example of a valent arc transitive graph with nonabelian vertex stabilizer A VALENT HALF ARC TRANSITIVE GRAPH

A classi cation of all arc transitive graphs of order a product of two primes is given Furthermore it is shown that cycles and complete graphs are the only arc transitive Cayley graph of abelian group of odd order Introductory remarks Throughout this paper graphs are nite simple and undirected By p and q we shall always denote prime numbers A k arc in a graph X is a sequence of k vertices v v v...

A cycle decomposition of a graph Γ is a set C of cycles of Γ such that every edge of Γ belongs to exactly one cycle in C. Such a decomposition is called arc-transitive if the group of automorphisms of Γ that preserve C setwise acts transitively on the arcs of Γ . In this paper, we study arc-transitive cycle decompositions of tetravalent graphs. In particular, we are interested in determining an...

A graph is half-arc-transitive if its automorphism group acts transitively on vertices and edges, but not on arcs. Let p be a prime. Cheng and Oxley [On weakly symmetric graphs of order twice a prime, J. Combin. Theory B 42(1987) 196-211] proved that there is no half-arc-transitive graph of order 2p, and Alspach and Xu [ 12 -transitive graphs of order 3p, J. Algebraic Combin. 3(1994) 347-355] c...

A subgroup of the automorphism group a graph acts half-arc-transitively on if it transitively vertex-set and edge-set but not arc-set graph. If full half-arc-transitively, is said to be half-arc-transitive. In 1994 Gardiner Praeger introduced two families tetravalent arc-transitive graphs, called C±1 C±ε that play prominent role in characterization graphs admitting an automorphisms with normal ...

A subgroup G of automorphisms of a graph X is said to be 2 -arc-transitive if it is vertexand edgebut not arc-transitive. The graph X is said to be 2 -arc-transitive if Aut X is 1 2 -arc-transitive. The interplay of two different concepts, maps and hypermaps on one side and 2 -arc-transitive group actions on graphs on the other, is investigated. The correspondence between regular maps and 2 -ar...

A 1 2 -arc-transitive graph is a vertexand edgebut not arc-transitive graph. In all known constructions of quartic 1 2 -arc-transitive graphs, vertex stabilizers are isomorphic to Z 2,Z 2 2 or to D8. In this article, for each positive integer m ≥ 1, an infinite family of quartic 1 2 -arctransitive graphs having vertex stabilizers isomorphic to Z m