Abstract: A vertex subset D of
a graph is called a perfect dominating set
of G if any vertex v
of G not in D
is adjacent to exactly one elementof
D. The perfect domination number is the minimum cardinality of a
perfect dominating set of G. A minimum
perfect dominating set of a graph G is
called a
-set of G. With the graph G,
we can associate a graph, denoted by called
-graph or perfect dominating set graph of G
as follows: is the set of all
-sets of G and two
-sets S and D
of G are adjacent in if and only if In this paper, we initiate a study
on
-graph of G.
Keywords and phrases: graphs,
-graphs, domination, perfect domination.
