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

Abstract

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.