Locally s -distance transitive graphs and pairwise transitive designs
نویسندگان
چکیده
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...
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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...
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In a previous work, the authors found new families of linear binary completely regular codes with the covering radius ρ = 3 and ρ = 4. In this paper, the automorphism groups of such codes are computed and it is proven that the codes are not only completely regular, but also completely transitive. From these completely transitive codes, in the usual way, i.e., as coset graphs, new presentations ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2013
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2013.07.003