Trees with the seven smallest and eight greatest Harary indices

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, we determined the first up to seventh smallest Harary indices of trees of order n≥16n≥16 and the first up to eighth greatest Harary indices of trees of order n≥14n≥14.

► The extremal trees are characterized with respect to Harary index. ► The trees with seven smallest Harary indices are determined. ► The trees with eight greatest Harary indices are determined.