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Graphs with a locally linear group of automorphisms

Published online by Cambridge University Press:  24 October 2008

V. I. Trofimov  and
R. M. Weiss
V. I. Trofimov
Affiliation:
Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ural Branch 620066 Ekaterinburg, Russia
R. M. Weiss
Affiliation:
Department of Mathematics, Tufts University, Medford, MA 02155, USA
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Let Γ be an undirected graph, V(Γ) the vertex set of Γ and G a subgroup of aut(Γ). For each vertex x ↦ V(Γ), let Γx denote the set of vertices adjacent to x in Γ and the permutation group induced on Γx. by the stabilizer Gx. For each i ≥ 1, will denote the pointwise stabilizer in Gx of the set of vertices at distance at most i from x in Γ. Let

for each i ≥ 1 and any set of vertices x, y, …, z of Γ. An s-path (or s-arc) is an (s + 1)-tuple (x0, x1, … xs) of vertices such that xi ↦ Γxi–1 for 1 ≤ i ≤ s and xi ╪ xi–2 for 2 ≤ i ≤ s.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 2 , September 1995 , pp. 191 - 206
Copyright
Copyright © Cambridge Philosophical Society 1995

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