We give a unified approach to analysing, for each positive integer s, a class of finite connected graphs that contains all the distance transitive graphs as well as the locally s-arc transitiveâ€¦ (More)

A linear space S is homogeneous if, whenever the linear structures induced on two finite subsets S$ and S" are isomorphic, there is at least one automorphism of S mapping S$ onto S". If everyâ€¦ (More)

The subdivision graph S(Î£) of a graph Î£ is obtained from Î£ by â€˜adding a vertexâ€™ in the middle of every edge of Î£ . Various symmetry properties of S(Î£) are studied. We prove that, for a connectedâ€¦ (More)

We define four families of geometries with as point graph the graph â€” or its complement â€” of all elliptic hyperplanes of a given parabolic quadric in any finite 6-dimensional projective space, whereâ€¦ (More)

The subdivision graph S(Î£) of a connected graph Î£ is constructed by adding a vertex in the middle of each edge. In a previous paper written with Cheryl E. Praeger, we characterised the graphs Î£ suchâ€¦ (More)

Two different constructions are given of a rank 8 arc-transitive graphwith 165 vertices and valency 8,whose automorphismgroup isM11. One involves 3-subsets of an 11-set while the other involvesâ€¦ (More)

A semilinear space S is a non-empty set of elements called points, provided with a collection of subsets called lines such that any pair of points is contained in at most one line and every lineâ€¦ (More)

We construct and analyse interesting integer valued functions on the points of a generalised quadrangle which lie in the orthogonal complement of a principal eigenspace of the collinearity relation.â€¦ (More)