منابع مشابه
Locally s-distance transitive graphs
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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We present a new approach to analysing finite graphs which admit a vertex intransitive group of automorphisms G and are either locally (G, s)– arc transitive for s ≥ 2 or G–locally primitive. Such graphs are bipartite with the two parts of the bipartition being the orbits of G. Given a normal subgroup N which is intransitive on both parts of the bipartition, we show that taking quotients with r...
متن کاملLocally s - arc transitive graphs with two different quasiprimitive actions ?
Previous work of the authors has shown that an important class of locally (G, 2)arc transitive graphs are those for which G acts faithfully and quasiprimitively on each of its two orbits on vertices. In this paper we give a complete classification in the case where the two quasiprimitive actions of G are of different types. The graphs obtained have amalgams previously unknown to the authors and...
متن کاملOn Distance-transitive Graphs
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 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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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2011
ISSN: 0364-9024
DOI: 10.1002/jgt.20574