Non-Split Perfect Triple Connected Domination Number of Different Product of Paths

A graph G is said to be triple connected if any three vertices lie on a path in G. The concept of triple connected domination number was introduced by J. Paulraj Joseph et.al. recently. A dominating set S is said to be triple connected dominating set, if the sub graph (S) is triple connected. The minimum cardinality taken over all triple connected dominating sets is called triple connected domination number of a graph G and it is denoted by γtc(G). Motivated by the above recently the concept of non-split perfect triple connected domination number was introduced in [1]. A subset S of V of a non-trivial graph G is said to be non-split perfect triple connected dominating set, if S is a triple connected dominating set and (V - S) is connected and has at least one perfect matching. The minimum cardinality taken over all non-split perfect triple connected sets in G is called the non-split perfect triple connected domination number of G and is denoted by γnsptc(G). In this paper we investigate this number for different product of the paths.