SPLIT AND EQUITABLE DOMINATION IN BOOK GRAPH AND STACKED BOOK GRAPH
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Published:
Jul 30, 2017
Keywords:
Domination, Cartesian Product graph, Split Domination, Equitable domination, Book Graph, Stacked Book Graph.
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Abstract
A subset D of V (G) is called an equitable dominating set of a graph G if for every v ∈ (V − D), there exists a vertex u ∈ D such that uv ∈ E(G) and |deg(u) − deg(v)| ≤ 1. The minimum cardinality of such a dominating set is denoted by γ^e (G) and is called equitable domination number of G. A dominating set D of graph G is called a split dominating set, if the induced sub graph is disconnected. In this paper first we introduce split domination in Book graph〖 B〗_n and stacked book graph B_(3,n). Later we prove the results for the equitable domination in B_n (V-D) .
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