Reserved Domination Number of some Graphs
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Abstract
In this paper the definitions of Reserved domination number and 2-reserved domination number are 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 ofand is denoted by where 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 and Complete Bipartite graph are found.
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