Reconfiguration of Minimum PSD Forcing Sets and Minimum Skew Forcing Sets

2025/01/07 by Bong, Novi, Flagg, Mary, Hunnell, Mark +4 · 2 citations
#05C50 #05C57 #05C69 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.03642

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.

Cited by

• Zero forcing propagation time intervals and graphs with fixed propagation time
• Universal perspectives on irredundance for X-set parameters

Related

• Power domination reconfiguration
• TAR reconfiguration for vertex set parameters
• Reconfiguration graphs for minimal domination sets
• Shortest Dominating Set Reconfiguration under Token Sliding
• Isomorphisms and properties of TAR reconfiguration graphs for zero forcing and other X-set parameters