Global equitable domination in some degree splitting graphs

S. K. Vaidya and R. M. Pandit
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 2, Pages 74—84
DOI: 10.7546/nntdm.2018.24.2.74-84
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Authors and affiliations

S. K. Vaidya
Department of Mathematics, Saurashtra University
Rajkot, Gujarat, India

R. M. Pandit
Department of Mathematics, Government Polytechnic
Jamnagar, Gujarat, India

Abstract

A dominating set is called a global dominating set if it is a dominating set of a graph G and its complement G. A subset D of V(G) is called an equitable dominating set if for every v ∈ V(G) − D, there exists a vertex u ∈ D such that uv ∈ E(G) and |d_G(u) − d_G(v)| ≤ 1. An equitable dominating set D of a graph G is a global equitable dominating set if it is also an equitable dominating set of the complement of G. The minimum cardinality of a global equitable dominating set of G is called the global equitable domination number of G which is denoted by γ^e_g(G). We explore this concept in the context of degree splitting graphs of some graphs.

Keywords

• Equitable dominating set
• Global equitable dominating set
• Global equitable domination number
• Degree splitting graph

2010 Mathematics Subject Classification

• 05C69

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