Symmetric graphs of diameter 2 with complete normal quotients Carmen Amarra University of Western Australia, Australia [email protected] A graph has diameter 2 if it is not a complete graph and if every pair of nonadjacent vertices is joined by a path of length 2. Our general problem is to examine the overall structure of graphs which are both arc-transitive and of diameter 2 using norm...

A finite group amalgam of index (k,m) is a 5-tuple (L,φ,B, ψ,R) where L, B, and R are finite groups, φ : B → L and ψ : B → R are monomorphisms, and the indices of B and B in L and R are k and m, respectively. The amalgam is faithful if N ≤ B, N C L, and N C R implies N = 1. It is well known that the finite faithful amalgams of index (k, 2) are in a bijective correspondence with (the conjugacy c...

A classification is given of finite graphs that are vertex primitive and 2arc regular. The classification involves various new constructions of interesting 2-arc transitive graphs.

We prove that, for a positive integer n and subgroup H of automorphisms of a cyclic group Z of order n, there is up to isomorphism a unique connected circulant digraph based on Z admitting an arc-transitive action of ZzH. We refine the Kovács–Li classification of arc-transitive circulants to determine those digraphs with automorphism group larger than ZzH. As an application we construct, for ea...

IS rel)re:se!otlng vertex-transitive as coset to allow us to obtain new results eral older results concerning the numbers transitive that are not 1 studied for more than a now, vertex-transitive graphs have quite great deal of activity. Their rich groups of automorphisms make from both the point of view of groups as well as of combinatorics. Among the most recent achievements, we can mention th...

A circulant is a Cayley digraph over a finite cyclic group. The classification of arc-transitive circulants is shown. The result follows from earlier descriptions of Schur rings over cyclic groups.