Infinite primitive directed graphs
Simon M. Smith
DOI: 10.1007/s10801-009-0190-3
Abstract
A group G of permutations of a set Ω is primitive if it acts transitively on Ω , and the only G-invariant equivalence relations on Ω are the trivial and universal relations.
A digraph Γ is primitive if its automorphism group acts primitively on its vertex set, and is infinite if its vertex set is infinite. It has connectivity one if it is connected and there exists a vertex α of Γ , such that the induced digraph Γ \setminus { α } is not connected. If Γ has connectivity one, a lobe of Γ is a connected subgraph that is maximal subject to the condition that it does not have connectivity one. Primitive graphs (and thus digraphs) with connectivity one are necessarily infinite.
Pages: 131–141
Keywords: keywords primitive; graph; digraph; permutation; group; orbital graph; orbital digraph; block-cut-vertex tree
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