Advances and Applications in Discrete Mathematics
Volume 2, Issue 1, Pages 49 - 57
(July 2008)
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PERFECT
DOMINATING SET GRAPH OF A GRAPH G
B. Chaluvaraju (India) and K. A. Vidya (India)
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is called a perfect dominating set
of G if any vertex v
of G not in D
is adjacent to exactly one element of
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.