Extremal results on the Mostar index of trees with fixed parameters

Abstract

For a graph [Formula: see text], the Mostar index of [Formula: see text] is the sum of [Formula: see text] over all edges [Formula: see text] of [Formula: see text], where [Formula: see text] denotes the number of vertices of [Formula: see text] that have a smaller distance in [Formula: see text] to [Formula: see text] than to [Formula: see text], and analogously for [Formula: see text]. We determine all the graphs that maximize and minimize the Mostar index, respectively, over all trees in terms of some fixed parameters like the number of odd vertices, the number of vertices of degree two, and the number of pendent paths of fixed length.