Linear Groups and Distance-transitive Graphs
نویسندگان
چکیده
منابع مشابه
Distance Transitive Graphs and Finite Simple Groups
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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A fruitful way of studying groups is by means of their actions on graphs. A very special and interesting class of groups are the ones acting distance-transitively on some graph. A group G acting on a connected graph F = (VT, ET) is said to act distance-transitively if its action on each of the sets {(x, y)\ x, y e VT, d(x, y) = i} is transitive. Here VT and ET stand for the vertices and edges o...
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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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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1989
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(89)80013-7