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

TL;DR

This paper derives explicit formulas for the maximum domination number and minimum independence number among all forests with a given degree sequence, advancing understanding of graph parameters in forest structures.

Contribution

It provides the first closed-form formulas for these extremal parameters in forests with specified degree sequences.

Findings

Closed formulas for maximum domination number in forests.

Closed formulas for minimum independence number in forests.

Applicable to all forests with a 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.