This paper begins the classification of all edge-primitive 3-arc-transitive graphs by classifying such where automorphism group is an almost simple with socle alternating or sporadic group, and classical a vertex-stabiliser acting faithfully on set neighbours.

We characterize the automorphism groups of quasiprimitive 2-arc-transitive graphs of twisted wreath product type. This is a partial solution for a problem of Praeger regarding quasiprimitive 2-arc transitive graphs. The solution stimulates several further research problems regarding automorphism groups of edge-transitive Cayley graphs and digraphs.

A transitive decomposition of a graph is a partition of the edge set together with a group of automorphisms which transitively permutes the parts. In this paper we determine all transitive decompositions of the Johnson graphs such that the group preserving the partition is arc-transitive and acts primitively on the parts.

A graph is said to be 1 2-transitive if its automorphism group is ver-tex and edge but not arc-transitive. For each n 11, a 1 2-transitive graph of valency 4 and girth 6, with the automorphism group isomor-phic to A n Z 2 , is given.

A regular graph is called semisymmetric if it is edge-transitive but not vertex-transitive. It is proved that the Gray graph is the only cubic semisymmetric graph of order 2p3, where p 3 is a prime.

A regular graph is called semisymmetric if it is edge transitive but not vertex transitive It is proved that the Gray graph is the only cubic semisymmetric graph of order p where p is a prime

In early 2000’s, Rivest [Riv00,MR02] and Micali [MR02] introduced the notion of transitive signature, which allows a third party to generate a valid signature for a composed edge (vi, vk), from the signatures for two edges (vi, vj) and (vj , vk), and using the public key only. Since then, a number of works, including [MR02,BN02,Hoh03,SFSM05,BN05], have been devoted on transitive signatures. Mos...

This paper introduces a family of tetravalent graphs called rose window graphs, denoted by Rn(a, r), and investigates their symmetry properties. Four families of these graphs are shown to be edge-transitive and it is conjectured that every Rn(a, r) which is edge-transitive belongs to one of these families. Proofs and conjectures about the size of a dart-stabilizer and about regular maps contain...