Extremal Trees with Fixed Degree Sequence

The greedy tree $\mathcal{G}(D)$ and the $\mathcal{M}$-tree $\mathcal{M}(D)$ are known to be extremal among trees with degree sequence $D$ respect various graph invariants. This paper provides a general theorem that covers large family of invariants for which or is extremal. Many results, example on Wiener index, number subtrees, independent subsets matchings follow as corollaries, do some new results such rooted spanning forests, incidence energy solvability. We also extend our fixed set whose majorised by given $D$, has applications.