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CROSS RATIO GRAPHS

Published online by Cambridge University Press:  30 October 2001

A. GARDINER ,
CHERYL E. PRAEGER  and
SANMING ZHOU
A. GARDINER
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2T
CHERYL E. PRAEGER
Affiliation:
Department of Mathematics and Statistics, University of Western Australia, Nedlands, Perth, WA 6907, Australia
SANMING ZHOU
Affiliation:
Department of Mathematics and Statistics, University of Western Australia, Nedlands, Perth, WA 6907, Australia
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Abstract

A family of arc-transitive graphs is studied. The vertices of these graphs are ordered pairs of distinct points from a finite projective line, and adjacency is defined in terms of the cross ratio. A uniform description of the graphs is given, their automorphism groups are determined, the problem of isomorphism between graphs in the family is solved, some combinatorial properties are explored, and the graphs are characterised as a certain class of arc-transitive graphs. Some of these graphs have arisen as examples in studies of arc-transitive graphs with complete quotients and arc-transitive graphs which ‘almost cover’ a 2-arc transitive graph.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 257 - 272
Copyright
The London Mathematical Society 2001

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