Vertex-primitive digraphs having vertices with almost equal neighbourhoods
Pablo Spiga, Gabriel Verret

TL;DR
This paper investigates vertex-primitive digraphs with nearly identical neighborhoods, establishing a structural theorem and applying it to resolve a question about synchronising groups.
Contribution
It provides a new structural characterization of certain vertex-primitive digraphs and applies this to a problem in group theory related to synchronization.
Findings
Structural theorem for vertex-primitive digraphs with similar neighborhoods
Resolution of a question on synchronising groups by Araújo and Cameron
Insights into the structure of digraphs with almost equal neighborhoods
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\'ujo and Cameron about synchronising groups.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Graph Theory Research · graph theory and CDMA systems
