A general method in the theory of domination in graphs

Abstract

In this article, we present a method to derive inequalities involving various domination parameters in graphs. As an application, we determine several lower bounds for these domination parameters in trees in terms of the order and the number of leaves. Finally, we characterize the classes of extremal trees.

Keywords:

• tree
• domination
• irredundance
• distance domination
• connected domination
• total domination
• distance irredundance
• p-domination
• end domination
• weakly connected domination
• paired domination
• double domination
• p-tuple domination
• restrained domination
• weak domination

2000 AMS Subject Classification:

• 05C69

Acknowledgements

We would like to thank the anonymous referees for their remarks and suggestions that helped improving the quality of this article.