%0 Journal Article
%T Reconfiguring Minimum Independent Dominating Sets in Graphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Brewster, Richard C
%A Mynhardt, Christina M
%A Teshima, Laura E
%D 2024
%\ 09/01/2024
%V 9
%N 3
%P 389-411
%! Reconfiguring Minimum Independent Dominating Sets in Graphs
%K independent domination number
%K graph reconfiguration
%K i-graph
%R 10.22049/cco.2023.28965.1797
%X The independent domination number $i(G)$ of a graph $G$ is the minimum cardinality of a maximal independent set of $G$, also called an $i(G)$-set. The $i$-graph of $G$, denoted $\mathscr{I}(G)$, is the graph whose vertices correspond to the $i(G)$-sets, and where two $i(G)$-sets are adjacent if and only if they differ by two adjacent vertices. We show that not all graphs are $i$-graph realizable, that is, given a target graph $H$, there does not necessarily exist a seed graph $G$ such that $H \cong \mathscr{I}(G)$. Examples of such graphs include $K_{4}-e$ and $K_{2,3}$. We build a series of tools to show that known $i$-graphs can be used to construct new $i$-graphs and apply these results to build other classes of $i$-graphs, such as block graphs, hypercubes, forests, cacti, and unicyclic graphs.
%U http://comb-opt.azaruniv.ac.ir/article_14682_00b259f42904b5f195c552f0b64e33f8.pdf