A new look at twin reduction

TL;DR

This paper provides a new characterization of twin reduction in graphs, offering insights into the structure of automorphism groups through a novel equivalence relation on vertices.

Contribution

It introduces a new characterization of twin reduction and derives a structure theorem for automorphism groups based on this relation.

Findings

Characterization of twin reduction as an equivalence relation

Structure theorem for automorphism groups of graphs

New insights into graph symmetries

Abstract

Twin reduction defines an equivalence relation on the vertex set of a graph. I give a characterisation of this equivalence relation. A consequence is a structure theorem for the automorphism group of the graph.