Extremal Trees with Respect to Dominance Order

Abstract

Let \((T_i)_{i\geq 0}\) be a sequence of trees such that \(T_{i+1}\) arises by deleting the \(b_i\) vertices of degree \(\leq 1\) from \(T_i\). We determine those trees of given degree sequence or maximum degree for which the sequence \(b_0, b_1, \ldots\) is maximum or minimum with respect to the dominance order. As a consequence, we also determine trees of given degree sequence or maximum degree that are of maximum or minimum Balaban index.