bounding the domination number of a tree in terms of its annihilation number
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abstract
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 $nge 2$, $gamma(t)le frac{3a(t)+2}{4}$, and we characterize the trees achieving this bound.
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Journal title:
transactions on combinatoricsPublisher: university of isfahan
ISSN 2251-8657
volume 2
issue 1 2013
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