Author's: S. AMUTHA and N. SRIDHARAN
Pages: [69] - [79]
Received Date: September 26, 2012
Submitted by:
Let G be a simple graph with no isolated vertices. A subset
D of a vertex set is said to be a total dominating set of
G if for every vertex
there is a vertex
such that uv is an edge. The minimum
cardinality of a total dominating set is called the total domination
number of G and it is denoted by
If
then for every vertex
is well defined. For a vertex
is either equal to
or less than
or greater than
We get a partition
where
In this paper, we obtain a necessary and sufficient condition for a
vertex to be in We prove that if then the induced
subgraph
is not complete and
If
then
If
and
then we show that G is regular.
total dominating set, total domination number.