Reconfiguration of Minimum PSD Forcing Sets and Minimum Skew Forcing Sets

TL;DR

This paper studies the structure and properties of reconfiguration graphs related to minimum PSD and skew forcing sets, providing insights into their realizability and structural characteristics across various graph classes.

Contribution

It introduces a universal approach to analyze reconfiguration graphs for multiple graph parameters and compares results across different zero forcing variants.

Findings

Characterization of reconfiguration graphs for specific graph classes

Structural properties established for reconfiguration graphs

Comparison of reconfiguration graphs across zero forcing variants

Abstract

Reconfiguration graphs provide a way to represent relationships among solutions to a problem, and have been studied in many contexts. We investigate the reconfiguration graphs corresponding to minimum PSD forcing sets and minimum skew forcing sets. We present results for the structure and realizability of certain graph classes as token exchange and token sliding reconfiguration graphs. Additionally, we use a universal approach to establish structural properties for the reconfiguration graphs of many common graph parameters under these reconfiguration rules. Finally, we compare results on reconfiguration graphs for zero forcing variants.