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

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

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.

Jeremy Lyle | Sean Patterson

[1] Michael A. Henning,et al. Relating the annihilation number and the total domination number of a tree , 2013, Discret. Appl. Math..

[2] Odile Favaron,et al. Independence and 2-domination in trees , 2005, Australas. J Comb..

[3] Odile Favaron,et al. k-Domination and k-Independence in Graphs: A Survey , 2012, Graphs Comb..

[4] Yair Caro,et al. Degree sequence index strategy , 2012, Australas. J Comb..

[5] Lutz Volkmann,et al. Independence and k-domination in graphs , 2011, Int. J. Comput. Math..

[6] Yair Caro,et al. A note on the k-domination number of a graph , 1990 .

[7] Sean Patterson. 2-Domination and Annihilation Numbers , 2015 .

[8] Ermelinda DeLaViña,et al. Graffiti . pc on the 2-domination number of a graph , 2010 .

[9] Peter J. Slater,et al. Fundamentals of domination in graphs , 1998, Pure and applied mathematics.

[10] Michael A. Henning,et al. Relating the annihilation number and the 2-domination number of a tree , 2014, Discret. Math..

[11] Jan Kratochvíl,et al. Mod-2 Independence and Domination in Graphs , 1999, WG.