Reserved Domination Number of graphs

Abstract

In this paper the definitions of Reserved domination number is introduced as for the graph  a subset of is called a Reserved Dominating Set of if(i) be any nonempty proper subset of ;(ii) Every vertex in is adjacent to a vertex in . The dominating set is called a minimal reserved dominating set if no proper subset of containing is a dominating set.  The set  is called Reserved set.The minimum cardinality of a reserved dominating set of is called the reserved domination number of and is denoted by where isthe number of reserved vertices. Using these definitions the reserved domination number for Path graph , Cycle graph , Wheel graph , Star graph , Fan graph , Helm graph , Complete graph , Complete Bipartite graph , Antiprism graph and Ladder rung graph are found.