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Abstract
The concept of complete graphs with real life application was introduced in[17] and the Forbidden pairs and the existence of a dominating cycle was introduced in[19] . In this paper, We introduce a new domination parameter called girth domination number , That is, if all the edges of the girth graph are the edges of any other cycles in a graph G and let G is a connected graph then is the girth graph of G if , i j. 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 girth dominating set, if every vertex in V-S is adjacent to at least one vertex of girth graph is called the girth dominating set. The minimum cardinality taken over all girth dominating set is called the girth domination number and is denoted by .We determine this number for some standard graphs and obtain bounds for general graphs. Its relationship with other graph theoretical parameters are also investigated.
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