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.
Spiga, P., Verret, G. (2017). Vertex-primitive digraphs having vertices with almost equal neighbourhoods. EUROPEAN JOURNAL OF COMBINATORICS, 61, 235-241 [10.1016/j.ejc.2016.11.002].
Vertex-primitive digraphs having vertices with almost equal neighbourhoods
Spiga, P
;
2017
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.
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