2-Domination Number in Special Classes of Graphs

Abstract

A set is a k-dominating set in  if every vertex in not in has atleast k neighbour in . The k-domination number of , denoted by  is the minimum cardinality of a k-dominating set of . When , k-dominating set is a called 2-dominating set. A dominating set Swith the additional property that the subgraph induced by S contains a perfect matching is called a paired-dominating set. The k- domination number andpaired domination numberof Gare the minimum cardinality of a k -dominating set andthe minimum cardinality of a paired dominating set respectively of G.In this paper, we obtain2- domination numberand paired domination number for special classes of graphs such as path necklace, cycle necklace and complete necklace networks.Further, we determine a lower bound for 2-domination numberof special classes of graphs.