Abstract We prove a rank 3 criterion for the simple connectedness of certain subsets of buildings and we give two applications of this criterion. The first generalizes a result of Tits for Chevalley… Expand

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… Expand

The paper forms part of Australian Research Council Discovery grant DP0770915 held by the second, third and fourth authors which includes the Australian Research Fellowship of the second author.Expand

A partial linear space is a non-empty set of points, provided with a collection of subsets called lines such that any pair of points is contained in at most one line.Expand

We compare three transitivity properties of finite graphs, namely, for a positive integer $s$, $s$-distance transitivity, $s$-geodesic transitivity and $s$-arc transitivity. It is known that if a… Expand

We classify noncomplete prime valency graphs satisfying the property that their automorphism group is transitive on both the set of arcs and theSet of 2-geodesics.Expand