CLASSIFICATION OF TETRAVALENT -TRANSITIVE NONNORMAL CAYLEY GRAPHS OF FINITE SIMPLE GROUPS

5-Arc transitive cubic Cayley graphs on finite simple groups

In this paper, we determine all connected 5-arc transitive cubic Cayley graphs on the alternating group A47; there are only two such graphs (up to isomorphism). By earlier work of the authors, these are the only two nonnormal connected cubic arc-transitive Cayley graphs for finite nonbelian simple groups, and so this paper completes the classification of such non-normal Cayley graphs.

Tetravalent half-edge-transitive graphs and non-normal Cayley graphs

Distance Transitive Graphs and Finite Simple Groups

This paper represents the first step in the classification of finite primitive distance transitive graphs. In it we reduce the problem to the case where the automorphism group is either almost simple or affine. Let ^ be a simple, connected, undirected graph with vertex set Q. If oc, /? e Q, then d(a, j8) denotes the distance between a and /3 in §. Let G be some group of automorphisms of §. Then...

Tetravalent edge-transitive Cayley graphs with odd number of vertices

A characterisation is given of edge-transitive Cayley graphs of valency 4 on odd number of vertices. The characterisation is then applied to solve several problems in the area of edge-transitive graphs: answering a question proposed by Xu (1998) regarding normal Cayley graphs; providing a method for constructing edge-transitive graphs of valency 4 with arbitrarily large vertex-stabiliser; const...

Product of normal edge-transitive Cayley graphs

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.