Geodesic
The Smallest Harmonic Index of Trees with Given Maximum Degree
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 499-513

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The harmonic index of a graph G, denoted by H(G), is defined as the sum of weights 2/[d(u) + d(v)] over all edges uv of G, where d(u) denotes the degree of a vertex u. In this paper we establish a lower bound on the harmonic index of a tree T.
Keywords: harmonic index, trees 
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     title = {The {Smallest} {Harmonic} {Index} of {Trees} with {Given} {Maximum} {Degree}},
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Rasi, Reza; Sheikholeslami, Seyed Mahmoud. The Smallest Harmonic Index of Trees with Given Maximum Degree. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 499-513. http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a12/