On vosperian and superconnected vertex-transitive digraphs

TL;DR

This paper studies the structure of certain highly symmetric directed graphs where minimal cutsets are characterized by successors or predecessors of vertices, advancing understanding of their automorphism groups.

Contribution

It improves existing results on the structure of vertex-transitive digraphs with specific cutset properties, deepening theoretical understanding.

Findings

Characterization of digraphs with transitive automorphism groups and specific cutset structures

Enhanced structural theorems for vosperian and superconnected vertex-transitive digraphs

New classifications and properties of minimal cutsets in these digraphs

Abstract

We investigate the structure of a digraph having a transitive automorphism group where every cutset of minimal cardinality consists of all successors or all predecessors of some vertex. We improve most of the existing results in this area.