Results on Coregular Perfect Domination of Line Graph and Relation with Different Dominations of Graph

For any graph G = (V, E),the line graph L(G)of a graph G is a graph whose set of vertices is the union of set of edges of G in which two vertices of L(G) are adjacent if and only if the corresponding edges of G are adjacent. A dominating set D_1 ⊆ V[L(G)] is called coregular perfect dominating set, if the induced subgraph V[L(G)]-D_1 is regular. The minimum cardinality of vertices in such a set is called coregular perfect domination number in L(G) and is represented by γ_cop [L(G)]. In this Article, we study the graph theoretic properties of γ_cop [L(G)] and many bounds were obtained in terms of elements of G and its relationship with other domination parameters were found .Our investigation on this work is to establish the application oriented standard results in the field of domination theory for several kinds of new concepts which are playing an important role of application.