Journal of Pure and Applied Mathematics: Advances and Applications
OF A SIMPLE GRAPH G WITH 
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.
