Advances and Applications in Discrete Mathematics
Volume 27, Issue 2, Pages 249 - 264
(July 2021) http://dx.doi.org/10.17654/DM027020249 |
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2-RESERVED DOMINATION NUMBER OF GRAPHS
G. Rajasekar and Govindan Rajasekar
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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 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. |
Keywords and phrases: 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.
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