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Reconfiguring Minimum Independent Dominating Sets in Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 1، دوره 9، شماره 3، آذر 2024، صفحه 389-411 اصل مقاله (740.93 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28965.1797 | ||
| نویسندگان | ||
| Richard C Brewster1؛ Christina M Mynhardt* 2؛ Laura E Teshima2 | ||
| 1Department of Mathematics and Statistics, Thompson Rivers University, 805 TRU Way, Kamloops, B.C., Canada | ||
| 2Department of Mathematics and Statistics, University of Victoria, PO BOX 1700 STN CSC, Victoria, B.C. Canada | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| independent domination number؛ graph reconfiguration؛ i-graph | ||
| مراجع | ||
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