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 |dG(u) − dG(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 γeg(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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Vaidya, S. K. & Pandit, R. M. (2018). Global equitable domination in some degree splitting graphs. Notes on Number Theory and Discrete Mathematics, 24(2), 74-84, doi: 10.7546/nntdm.2018.24.2.74-84.