TY - JOUR

T1 - Cross ratio graphs

AU - Gardiner, Anthony

AU - Praeger, CE

AU - Zhou, S

PY - 2001/10/1

Y1 - 2001/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77958082156&partnerID=8YFLogxK

U2 - 10.1112/S0024610701002150

DO - 10.1112/S0024610701002150

M3 - Article

SN - 1469-7750

SN - 1469-7750

SN - 1469-7750

SN - 1469-7750

SN - 1469-7750

SN - 1469-7750

SN - 1469-7750

SN - 1469-7750

SN - 1469-7750

SN - 1469-7750

SN - 1469-7750

SN - 1469-7750

VL - 64

SP - 257

EP - 272

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

ER -