@article {
author = {Brewster, Richard and Mynhardt, Christina and Teshima, Laura},
title = {Reconfiguring Minimum Independent Dominating Sets in Graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {9},
number = {3},
pages = {389-411},
year = {2024},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2023.28965.1797},
abstract = {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.},
keywords = {independent domination number,graph reconfiguration,i-graph},
url = {http://comb-opt.azaruniv.ac.ir/article_14682.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14682_00b259f42904b5f195c552f0b64e33f8.pdf}
}