Outer perfect connected at-most twin domination number of a graph

Recently in [2], G. Mahadevan et.al., introduced the concept of at most twin outer perfect domination number of a graph. By imposing an additional constraint on its complement, we introduce a new parameter called Outer perfect connected at most twin domination number of a graph. A set S⊆V(G) is said to be an Outer perfect connected at most twin dominating set (OPCATD-set) of G, if every vertex v∈V−S,1≤N(v)∩S≤2 and is connected as well as has a perfect matching. The minimum cardinality of OPCATD-set is called Outer perfect connected at most twin domination number and it is denoted by ɣopcat(G). In this paper we investigate this number for some standard graphs and find the relationship between this parameter with other graph theoretical parameter.