A Note on the Annihilation Number and 2-domination Number of a Tree

Document Type

Article

Publication Date

4-2017

Department

Biological Sciences

School

Biological, Environmental, and Earth Sciences

Abstract

In 2014, Desormeaux et al. (Discrete Math 319:15–23, 2014) proved a relationship between the annihilation number and 2-domination number of a tree. In this note, we provide a family of bounds for the 2-domination number of a tree based on the amount of vertices of small degree. This family of bounds extends current bounds on the 2-domination number of a tree, and provides an alternative proof for the relationship between the annihilation number and the 2-domination number of a tree that was shown by Desormeaux et al.

Publication Title

Journal of Combinatorial Optimization

Volume

33

Issue

3

First Page

968

Last Page

976

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