Resumen
For a graph ??=(??,??)
G
=
(
V
,
E
)
, the ??
?
-graph of G, denoted ??(??)=(??(??),??(??))
G
(
?
)
=
(
V
(
?
)
,
E
(
?
)
)
, is the graph whose vertex set is the collection of minimum dominating sets, or ??
?
-sets of G, and two ??
?
-sets are adjacent in ??(??)
G
(
?
)
if they differ by a single vertex and the two different vertices are adjacent in G. In this paper, we consider ??
?
-graphs of trees. We develop an algorithm for determining the ??
?
-graph of a tree, characterize which trees are ??
?
-graphs of trees, and further comment on the structure of ??
?
-graphs of trees and its connections with Cartesian product graphs, the set of graphs which can be obtained from the Cartesian product of graphs of order at least two.