Vertex-primitive digraphs having vertices with almost equal neighbourhoods

Pablo Spiga; Gabriel Verret

doi:10.1016/j.ejc.2016.11.002

Vertex-primitive digraphs having vertices with almost equal neighbourhoods

Pablo Spiga, Gabriel Verret

Research output: Contribution to journal › Article

1 Citation (Scopus)

Abstract

We consider vertex-primitive digraphs having two vertices with almost equal neighbourhoods (that is, the set of vertices that are neighbours of one but not the other is small). We prove a structural result about such digraphs and then apply it to answer a question of Araújo and Cameron about synchronising groups.

Original language	English
Pages (from-to)	235-241
Number of pages	7
Journal	European Journal of Combinatorics
Volume	61
DOIs	https://doi.org/10.1016/j.ejc.2016.11.002
Publication status	Published - 1 Mar 2017

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title = "Vertex-primitive digraphs having vertices with almost equal neighbourhoods",

abstract = "We consider vertex-primitive digraphs having two vertices with almost equal neighbourhoods (that is, the set of vertices that are neighbours of one but not the other is small). We prove a structural result about such digraphs and then apply it to answer a question of Ara{\'u}jo and Cameron about synchronising groups.",

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AU - Verret, Gabriel

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AB - We consider vertex-primitive digraphs having two vertices with almost equal neighbourhoods (that is, the set of vertices that are neighbours of one but not the other is small). We prove a structural result about such digraphs and then apply it to answer a question of Araújo and Cameron about synchronising groups.

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