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Journal of Combinatorial Optimization

, Volume 33, Issue 3, pp 968–976 | Cite as

A note on the annihilation number and 2-domination number of a tree

  • Jeremy Lyle
  • Sean Patterson
Article

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.

Keywords

Annihilation number 2-Domination number Trees 

Mathematics Subject Classification

05C35 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.The University of Southern MississippiHattiesburgUSA
  2. 2.Olivet Nazarene UniversityBourbonnaisUSA

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