New Implementation of Paired Triple Connected Domination Number of a Graph

A set S V is a paired triple connected dominating set if S is a triple connected dominating set of G and the induced subgraph has a perfect matching. The paired triple connected domination number ptc (G) is the minimum cardinality taken over all paired triple connected dominating sets in G. The minimum number of colours required to colour all the vertices so that adjacent vertices do not receive the same colour and is denoted by. In [5], Mahadevan G et. al. , characterized the classes of the graphs whose sum of paired triple connected domination number and chromatic number equals 2n 1. In this paper we characterize the classes of all graphs whose sum of paired triple connected domination number and chromatic number equals to 2n 2, 2n 3, 2n 4, for any n 5.