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arxiv: 1507.04650 · v1 · pith:OQND3K7Cnew · submitted 2015-07-16 · 🧮 math.CO

Largest Domination Number and Smallest Independence Number of Forests with given Degree Sequence

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keywords numberalphagammasequencedegreedominationforestsindependence
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For a sequence $d$ of non-negative integers, let ${\cal F}(d)$ be the set of all forests whose degree sequence is $d$. We present closed formulas for $\gamma_{\max}^{\cal F}(d)=\max\{ \gamma(F):F\in {\cal F}(d)\}$ and $\alpha_{\min}^{\cal F}(d)=\min\{ \alpha(F):F\in {\cal F}(d)\}$ where $\gamma(F)$ and $\alpha(F)$ are the domination number and the independence number of a forest $F$, respectively.

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