A line graph L(G) is the graph whose vertices corresponding to the graph G and two vertices in L(G) are adjacent if and only if the corresponding edges in G are adjacent. A dominating set D⊆V[L(G)] is known as coregularConnected dominating set , if the induced sub graph 〈D〉 is connected such that the induced subgraph < V[L(G)]-D> is regular. The minimum cardinality of vertices in such a set is called coregular Connected domination number in L(G) , and is denoted by γ_coc [L(G)].