Irredundant Complete Domination Number of Graphs

The concept of complete graphs with real life application was introduced in [17] .In [14]
, A. Nellai Murugan et.al., was
introduced the concept of complete dominating number of a graph. In this paper, We introduce a new domination
parameter called Irredundant complete dominating set of K4 -e , A subset S of V of a non trivial graph G is called a
dominating set of G if every vertex in V-S is adjacent to at least one vertex in S. The domination number of G is
the minimum cardinality taken over all dominating set in G. A subset S of V of a nontrivial graph G is said to be
complete dominating set, If for each denoted by S’ is the complete dominating set.
The minimum cardinality taken over all complete dominating set is called the complete domination number and is
denoted by
[14].A set is said to be redundant in S if othewise x is said to be irredundant
in S . Finally , S is called an irredundant set if all are irredundant in S , Otherwise S is a redundant set .A subset S
of v of a nontrivial graph G is said to be an Irredundant complete dominating set if S is an irredundant and complete .
The minimum cardinality taken over all an irredundant complete dominating set is called an Irredundant complete
domination number and is denoted by .
Mathematics Subject Classification: 05C69