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

Jeremy Lyle () and Sean Patterson
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Jeremy Lyle: The University of Southern Mississippi
Sean Patterson: The University of Southern Mississippi

Journal of Combinatorial Optimization, 2017, vol. 33, issue 3, No 11, 968-976

Abstract: 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; 05C35 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0019-7

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