Interrogation for Modernistic Conceptualization of Complementary Perfect Hop Domination Number with Various Grid Models

In this paper, we introduce the concept of Complementary perfect hop domination number of a graph. A set S ⊆ V is a hop dominating set of G, if every vertex v ∈ V − S there exists u ∈ S such that d(u,v) = 2. A set S ⊆ V is a complementary perfect hop dominating set of G if S is a hop dominating set and has atleast one perfect matching. The minimum cardinality of complementary perfect hop dominating set is called complementary perfect hop domination number of G and it is denoted by CPHD(G). Here, we investigate this CPHD number for some mirror graphs and some special type of graphs.