Abstract

For a graph G, its variable sum exdeg index is defined as SEI a G = ∑ x y ∈ E G a d x + a d y, where a is a real number other than 1 and d x is the degree of a vertex x. In this paper, we characterize all trees on n vertices with first three maximum and first three minimum values of the SEI a index. Also, we determine all the trees of order n with given diameter d and having first three largest values of the SEI a index.