منابع مشابه
Finite primitive distance-transitive graphs
The status of the project of classifying finite primitive distance-transitive graphs is surveyed. Particular attention is given to the structure of the proof of the recently obtained classification of finite primitive affine distance-transitive graphs. © 2005 Elsevier Ltd. All rights reserved.
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This paper represents the first step in the classification of finite primitive distance transitive graphs. In it we reduce the problem to the case where the automorphism group is either almost simple or affine. Let ^ be a simple, connected, undirected graph with vertex set Q. If oc, /? e Q, then d(a, j8) denotes the distance between a and /3 in §. Let G be some group of automorphisms of §. Then...
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Cameron's proof of this result is based on Sims' Conjecture, which has only been shown to hold using the classification of finite simple groups. In the final section of [1], Cameron indicates how Theorem 1 might be proved in an elementary fashion using Macpherson's classification of infinite distance-transitive graphs of finite valency [4]. Corollary 1 below provides the missing portion of this...
متن کاملFinite two-distance-transitive graphs of valency 6
A non-complete graph Γ is said to be (G, 2)-distance-transitive if, for i = 1, 2 and for any two vertex pairs (u1, v1) and (u2, v2) with dΓ(u1, v1) = dΓ(u2, v2) = i, there exists g ∈ G such that (u1, v1) = (u2, v2). This paper classifies the family of (G, 2)-distancetransitive graphs of valency 6 which are not (G, 2)-arc-transitive.
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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 transitive graphs of diameter at least s. A graph is in the class if it is connected and if, for each vertex v, the subgroup of automorphisms fixing v acts transitively on the set of vertices at distance i from v, ...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2017
ISSN: 0364-9024
DOI: 10.1002/jgt.22112