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An application of p-factorization methods to symmetric graphs

Published online by Cambridge University Press:  24 October 2008

Richard Weiss
Richard Weiss
Affiliation:
Freie Universität Berlin, W. Germany
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Let Γ be an undirected graph and G a subgroup of aut (Γ) acting transitively on the vertex set V(Γ) of Γ. Let x be an arbitrary vertex of Γ. We denote by T(x) the set of vertices adjacent to x and by G(x)Γ(x) the permutation group induced by the stabilizer G(x) of x in G on Γ(x); G(x)Γ(x) is called the subconstituent of G (with respect to Γ). Let G1(x) = {a ∈ G(x)|a ∈ G(y) for each y ∈ Γ(x)}. For each y ∈ Γ(x), let G(x, y) = G(x) ∩ G(y) and G1(x, y) = G1(x) ∩ G1(y). An s-path is an (s+ l)-tuple (x0, x1, …, xs) of vertices such that xi−1 ∈ Γ(xi) if 1 ≤ i ≤ s and xi−2 ≠ xi if 2 ≤ i ≤ s. Γ is called (G, s)-transitive if G acts transitively on the set of all s-paths but intransitively on the set of all (S+1)-paths in Γ.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 1 , January 1979 , pp. 43 - 48
Copyright
Copyright © Cambridge Philosophical Society 1979

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