Original Articles

Bounds on the Global Domination Number

Published in: Quaestiones Mathematicae
Volume 38 , issue 4 , 2015 , pages: 563–572

DOI: 10.2989/16073606.2014.981728

Author(s): Wyatt J. Desormeaux Department of Mathematics, South Africa , Philip E. Gibson Department of Mathematics and Statistics, USA , Teresa W. Haynes Department of Mathematics, South Africa

Keywords: 05C69 , 05C69

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Abstract

A set S of vertices in a graph G is a global dominating set of G if S simultaneously dominates both G and its complement Ḡ. The minimum cardinality of a global dominating set of G is the global domination number of G. We determine bounds on the global domination number of a graph and relationships between it and other domination related parameters.

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