Abstract: Let be
a graph. A set is
called a perfect dominating set if every vertex in is
adjacent to exactly one vertex in D. A
perfect dominating set D is said to be
connected cutfree perfect dominating set if the induced subgraph of
G is a connected graph having no
cutvertex. D is called a block perfect
dominating set if is
a block in G. The connected cutfree perfect domination number is
the minimum cardinality taken over all minimal connected cutfree perfect
dominating sets and the block perfect dominating number is the minimum cardinality taken over all minimal block
perfect dominating sets in G. In this
paper, we study the properties of these two perfect domination numbers and
investigate their relationships with other domination parameters.
