Characterization of induced paired domination number of a graph

The concept of induced paired domination number of a graph was introduced by D.S.Studer, T.W. Haynes and L.M. Lawson11, with the following application in mind. In the guard application an induced paired dominating set represents a configuration of security guards in which each guard is assigned one other as a designated backup with in (as in a paired dominating set), but to avoid conflicts (such as radio interference) between a guard and his/her backup, we require that the backup each guard be unique. Since among the guards only designated partners are adjacent to each other, we reduce the possibility of conflicts in communication. A set S V is a induced -paired dominating set if S is a dominating set of G and the induced subgraph is a set of independent edges. The induced paired domination number ip(G) is the minimum cardinality taken over all induced paired 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 . Mahadevan3-5 G, characterized the classes of all graphs whose sum of induced paired domination number and chromatic number of order up to 2n 5. In this paper we characterize the classes of all graphs whose sum of induced paired domination number and chromatic number equals to 2n 6, for any n  4.