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 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 source graph G such that H is isomorphic to
I(G). Examples of such graphs include K4ββe and K2,3β. 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.Comment: 22 pages, 9 figure