Szeged index, edge Szeged index, and semi-star trees

A semi-star tree is a star tree whose some edges may be replaced by paths of length more than one. In this paper we present some increasing and decreasing transformations for Szeged index of the semi-star trees. Then we introduce palm semi-star tree and uniform semi-star tree and show that they are extremal with respect to the Szeged index and edge Szeged index. In addition, we investigate the relation between the Szeged index and edge Szeged index for all trees.