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On the simple connectedness of certain subsets of buildings
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 ChevalleyExpand
An infinite family of biquasiprimitive 2-arc transitive cubic 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 ofExpand
Locally s-distance transitive graphs
TLDR
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
Local 2-geodesic transitivity and clique graphs
TLDR
A 2-geodesic in a graph is a vertex triple (u,v,w) such that v is adjacent to both u and w and u,w are not adjacent. Expand
On imprimitive rank 3 permutation groups
TLDR
A classification is given of rank 3 group actions which are quasiprim- itive but not primitive. Expand
On imprimitive rank 3 permutation groups
TLDR
A classification is given of rank 3 group actions which are quasiprim-itive but not primitive. Expand
A classification of finite partial linear spaces with a primitive rank 3 automorphism group of grid type
TLDR
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
Some graphs related to the small Mathieu groups
TLDR
Two different constructions are given of a rank 8 arc-transitive graph with 165 vertices and valency 8, whose automorphism group is M"1"1. Expand
On distance, geodesic and arc transitivity of graphs
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 aExpand
Finite 2-Geodesic Transitive Graphs of Prime Valency
TLDR
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
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