In this paper the definitions of reserved domination number and 2-reserved domination number are introduced as for the graph G = (V, E). A subset S of V is called a reserved dominating set (RDG) of G if (i) μ is any nonempty proper subset of S; (ii) Every vertex in V − S is adjacent to a vertex in S. The dominating set S is called a minimal reserved dominating set if no proper subset of S containing μ is a dominating set. The set μ is called reserved set. The minimum cardinality of a reserved dominating set of G is called the reserved domination number of G and is denoted by where 2 is the number of reserved vertices. Using these definitions the 2-reserved domination number for Path graph Cycle graph Wheel graph  Star graph  Fan graph  Complete graph  Complete Bipartite graph  and Pan graph  are found.

dominating set, reserved dominating set, 2-reserved dominating set, reserved domination number, 2-reserved domination number, path, cycle, wheel, star, fan, complete, complete bipartite, Pan.