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	Volume 4, Issue 2 Pg 95 - 186 (October 2009)
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Advances and Applications in Discrete Mathematics

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.

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)

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

Keywords and phrases: graph, perfect domination number, connected cutfree perfect domination number, block perfect domination number.

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