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Equitable Domination In Graphs by A. ANITHA; S. ARUMUGAM; MUSTAPHA CHELLALI is a Computer Science article available to read on EtoBox.

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Let D be a dominating set of a graph G = (V, E). For v ∈ D, let n~1~(v) = |N(v) ∩ (V - D)| and for w ∈ V - D, let n~2~(w) = |N(w) ∩ D|. Then D is called an equitable dominating set of type 1 if |n~1~(v~1~) - n~1~(v~2~)| ≤ 1 for all v~1~, v~2~ ∈ D and is called an equitable dominating set of type 2 if |n~2~(w~1~) - n~2~(w~2~)| ≤ 1 for all w~1~, w~2~ ∈ V - D. The minimum cardinality of an equitable dominating set of G of type 1 (type 2) is called the 1-equitable (2-equitable) domination number of G and is denoted by γ ~eq1~ (G)(γ ~eq2~ (G)). If D is an equitable dominating set of type 1 and type 2, then D is called an equitable dominating set and the equitable domination number of G is defined to be the minimum cardinality of an equitable dominating set and is denoted by γ ~eq~ (G). In this paper we initiate a study of these parameters.

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Author

A. ANITHA; S. ARUMUGAM; MUSTAPHA CHELLALI

Publisher

World Scientific Pub Co Pte Lt

Published

2011

Language

EN

Field

Computer Science (Physical Sciences)