NDLI: Infinite primitive directed graphs

Content Provider	Springer Nature Link
Author	Smith, Simon M.
Copyright Year	2009
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∖{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.The primitive graphs with connectivity one have been fully classified by Jung and Watkins: the lobes of such graphs are primitive, pairwise-isomorphic and have at least three vertices. When one considers the general case of a primitive digraph with connectivity one, however, this result no longer holds. In this paper we investigate the structure of these digraphs, and obtain a complete characterisation.
Starting Page	131
Ending Page	141
Page Count	11
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	31
Issue Number	1
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2009-07-28
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Primitive Graph Digraph Permutation Group Orbital graph Orbital digraph Block-cut-vertex tree Group Theory and Generalizations Computer Science Order, Lattices, Ordered Algebraic Structures Convex and Discrete Geometry Combinatorics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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