Published Paper Details:

The concept of complete graphs with real life application was introduced in and the Forbidden pairs and the existence of a dominating cycle was introduced . In this paper, we introduce a new domination parameter called Restrained girth domination number , that is, if all the edges of the girth(cycle) 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 . 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 gamma(G) of G is the minimum cardinality taken over all dominating set in G. A subset S of V of any cyclic graph G is said to be a restrained girth dominating set, if every vertex in V-S is adjacent to at least one vertex of girth graph as well as another vertex in V-S is called the restrained girth dominating set. The minimum cardinality taken over all restrained girth dominating set is called the restrained girth domination number and is denoted by gamma_{rg}(G). We determine this number for some standard graphs and obtain bounds for general graphs. Its relationship with other graph theoretical parameters are also investigated.