68 research outputs found
Reconfiguration of Minimum Independent Dominating Sets in Graphs
The independent domination number of a graph is the minimum
cardinality of a maximal independent set of , also called an -set. The
-graph of , denoted , is the graph whose vertices
correspond to the -sets, and where two -sets are adjacent if and
only if they differ by two adjacent vertices. We show that not all graphs are
-graph realizable, that is, given a target graph , there does not
necessarily exist a source graph such that is isomorphic to
. Examples of such graphs include and . We
build a series of tools to show that known -graphs can be used to construct
new -graphs and apply these results to build other classes of -graphs,
such as block graphs, hypercubes, forests, cacti, and unicyclic graphs.Comment: 22 pages, 9 figure
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