2-switch transition on unicyclic graphs and pseudoforest

TL;DR

This paper proves that any two unicycle graphs or pseudoforests with the same degree sequence can be transformed into each other through a finite sequence of 2-switches, preserving their unicyclic or pseudoforest structure.

Contribution

It introduces a method to transform unicycle graphs and pseudoforests with identical degree sequences via 2-switches while maintaining their structural properties.

Findings

Any two unicycle graphs with the same degree sequence are connected through 2-switches.

The transformation preserves the unicyclic or pseudoforest structure throughout.

The result applies to graphs sharing the same degree sequence, ensuring structural integrity during transformation.

Abstract

In the present work we prove that given any two unicycle graphs (pseudoforests) that share the same degree sequence there is a finite sequence of 2-switches transforming one into the other such that all the graphs in the sequence are also unicyclic graphs (pseudoforests).