Advances and Applications in Discrete Mathematics
Volume 4, Issue 2, Pages 161 - 168
(October 2009)
|
|
THE BLOCK PERFECT DOMINATION NUMBER OF A GRAPH
S. R. Ramachandra (India) and N. D. Soner (India)
|
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.