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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## Details

### 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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## Cite this paper

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.