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.
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Lyle, J., Patterson, S. A note on the annihilation number and 2-domination number of a tree. J Comb Optim 33, 968–976 (2017). https://doi.org/10.1007/s10878-016-0019-7
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DOI: https://doi.org/10.1007/s10878-016-0019-7