TS-Reconfiguration of Dominating Sets in Circle and Circular-Arc Graphs

We study the dominating set reconfiguration problem with token sliding rule. Let G be a graph \(G=(V,E)\) and two sets \(D_s\) \(D_t\) of G. The goal is to decide if there exists sequence \(S=\langle D_1:=D_s,\ldots ,D_{\ell }:=D_t \rangle \) such that for any consecutive \(D_r\) \(D_{r+1}\) \(r<t\), \(D_{r+1}=(D_r\setminus u) \cup \{v \}\), where \(uv\in E\).