  A set D of vertices of a graph G=(V,E) is irredundant if each v of D
satisfies (a) v is isolated in the subgraph induced by D, or (b) v is adjacent
to a vertex in V-D that is nonadjacent to all other vertices in D. The upper
irredundance number IR(G) is the largest cardinality of an irredundant set of
G; an IR(G)-set is an irredundant set of cardinality IR(G). The IR-graph of G
has the IR(G)-sets as vertex set, and sets D and D' are adjacent if and only if
D' is obtained from D by exchanging a single vertex of D for an adjacent vertex
in D'. We study the realizability of graphs as IR-graphs and show that all
disconnected graphs are IR-graphs, but some connected graphs (e.g. stars of
order three or more, the paths of order 4 or 5, the 5-cycle) are not.
