A graph Γ is said to be locally (G, 2)-arc transitive for G a subgroup of Aut(Γ) if, for any vertex α of Γ, G is transitive on the 2-arcs of Γ starting at α. In this talk, we will discuss general results involving locally (G, 2)-arc transitive graphs and recent progress toward the classification of the locally (G, 2)-arc transitive graphs, where Sz(q) ≤ G ≤ Aut(Sz(q)), q = 2 for some k ∈ N. In ...

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 ...

This paper concerns finite, edge-transitive direct and strong products, as well as infinite weak Cartesian products. We prove that the direct product of two connected, non-bipartite graphs is edge-transitive if and only if both factors are edgetransitive and at least one is arc-transitive, or one factor is edge-transitive and the other is a complete graph with loops at each vertex. Also, a stro...

Given a graph Γ, perfect code in Γ is an independent set C of such that every vertex outside adjacent to unique and total vertices C. To study (total) codes vertex-transitive graphs, we generalize the concept subgroup finite group introduced by Huang et al. as follows: G H G, A containing called pair (G,H) if there exists coset Cos(G,H,U) consisting left cosets Cos(G,H,U). We give necessary suf...

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