Dehgardai, N., Norouzian, S., Sheikholeslami, S. (2013). Bounding the domination number of a tree in terms of its annihilation number. Transactions on Combinatorics, 2(1), 9-16.

Nasrin Dehgardai; Sepideh Norouzian; Seyed Mahmoud Sheikholeslami. "Bounding the domination number of a tree in terms of its annihilation number". Transactions on Combinatorics, 2, 1, 2013, 9-16.

Dehgardai, N., Norouzian, S., Sheikholeslami, S. (2013). 'Bounding the domination number of a tree in terms of its annihilation number', Transactions on Combinatorics, 2(1), pp. 9-16.

Dehgardai, N., Norouzian, S., Sheikholeslami, S. Bounding the domination number of a tree in terms of its annihilation number. Transactions on Combinatorics, 2013; 2(1): 9-16.

Bounding the domination number of a tree in terms of its annihilation number

A set $S$ of vertices in a graph $G$ is a dominating set if every vertex of $V-S$ is adjacent to some vertex in $S$. The domination number $\gamma(G)$ is the minimum cardinality of a dominating set in $G$. The annihilation number $a(G)$ is the largest integer $k$ such that the sum of the first $k$ terms of the non-decreasing degree sequence of $G$ is at most the number of edges in $G$. In this paper, we show that for any tree $T$ of order $n\ge 2$, $\gamma(T)\le \frac{3a(T)+2}{4}$, and we characterize the trees achieving this bound.

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