A graph is said to be symmetric if its automorphism group is transitive on its arcs. A complete classification is given of pentavalent symmetric graphs of order 24p for each prime p. It is shown that a connected pentavalent symmetric graph of order 24p exists if and only if p=2, 3, 5, 11 or 17, and up to isomorphism, there are only eleven such graphs.

A new infinite family of bipartite cubic 3-arc transitive graphs is constructed and studied. They provide the first known examples admitting a 2-arc transitive vertex-biquasiprimitive group of automorphisms for which the stabiliser of the biparts is not quasiprimitive on either bipart.

We establish natural bijections between three different classes of combinatorial objects; namely certain families of locally 2–arc transitive graphs, partial linear spaces, and homogeneous factorisations of arc-transitive graphs. Moreover, the bijections intertwine the actions of the relevant automorphism groups. Thus constructions in any of these areas provide examples for the others.

A regular edge but not vertex transitive graph is said to be semisym metric The study of semisymmetric graphs was initiated by Folkman who among others gave constructions of several in nite families such graphs In this paper a generalization of his construction for or ders a multiple of is proposed giving rise to some new families of semisymmetric graphs In particular one associated with the cy...

In 2017, Giudici, Li and the third author constructed first known family of vertex-primitive 2-arc-transitive digraphs valency at least 2. The smallest digraph in this admits PSL3(49) acting 2-arc-transitively with vertex-stabilizer A6 hence has 30758154560 vertices. paper, we prove that is 2 fewest

Let0 be a graph and G be a 2-arc transitive automorphism group of0. For a vertex x ∈ 0 let G(x)0(x) denote the permutation group induced by the stabilizer G(x) of x in G on the set 0(x) of vertices adjacent to x in 0. Then 0 is said to be a locally projective graph of type (n, q) if G(x)0(x) contains PSLn(q) as a normal subgroup in its natural doubly transitive action. Suppose that 0 is a local...

In this note, we construct bipartite 2-walk-regular graphs with exactly 6 distinct eigenvalues as the point-block incidence graphs of group divisible designs with the dual property. For many of them, we show that they are 2-arc-transitive dihedrants. We note that some of these graphs are not described in Du et al. (2008), in which they classified the connected 2-arc transitive dihedrants.