منابع مشابه
An Infinite Highly Arc-transitive Digraph
The main purpose of this note is to construct an infinite , highly arc-transitive digraph with finite out-valency , and with out-spread greater than 1 , which does not have the two-way infinite path Z as a homomorphic image . This answers Question 3 . 8 in the paper [3] of Cameron , Praeger and Wormald . Our digraph has infinite in-valency . By a result of Praeger (see [5]) , a connected , vert...
متن کاملAn infinite family of biquasiprimitive 2-arc transitive cubic graphs
A new infinite family of bipartite cubic 3-arc transitive graphs is constructed and studied. They provide the first known examples admitting a 2-arc transitive vertex-biquasiprimitive group of automorphisms for which the stabiliser of the biparts is not quasiprimitive on either bipart.
متن کاملCrown-free highly arc-transitive digraphs
We construct a family of infinite, non-locally finite highly arc-transitive digraphs which do not have universal reachability relation and which omit special digraphs called ‘crowns’. Moreover, there is no homomorphism from any of our digraphs onto Z. The methods are adapted from [5] and [6].
متن کاملHighly arc transitive digraphs: reachability, topological groups
Let D be a locally finite, connected, 1-arc transitive digraph. It is shown that the reachability relation is not universal in D provided that the stabilizer of an edge satisfies certain conditions which seem to be typical for highly arc transitive digraphs. As an implication, the reachability relation cannot be universal in highly arc transitive digraphs with prime inor out-degree. Two differe...
متن کاملHighly arc-transitive digraphs - Structure and counterexamples
Two problems of Cameron, Praeger, and Wormald [Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica (1993)] are resolved. First, locally finite highly arc-transitive digraphs with universal reachability relation are presented. Second, constructions of two-ended highly arc-transitive digraphs are provided, where each ‘building block’ is a finite bipartite digrap...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1997
ISSN: 0195-6698
DOI: 10.1006/eujc.1996.0099