Szeged-type bond additive indices are a class of distance-based topological indices defined by counting the vertices or edges that are closer to the end vertices of an edge. Important members of this family include the Szeged index, Mostar index, PI index, SPI index, and the Szeged–Sombor index, together with their corresponding edge versions. Although these indices have been extensively studied and extremal results have been obtained for various graph classes, a unified framework for their extremal analysis is still lacking.
In this paper, we introduce a unified approach for studying extremal problems of Szeged-type bond additive indices on trees. We show that, for 44 different Szedged type indices, the path and the star uniquely attain the extremal values of these indices. We also propose their exponential version of these indices and establish that the same graph attain the extremal values for trees in these distance based bond additive indices.