Authors: L. Zhong Title: The minimum harmonic index for unicyclic graphs with given diameter Source: Discussiones Mathematicae Graph Theory Received 20.07.2016, Revised 06.12.2016, Accepted 06.12.2016, doi: 10.7151/dmgt.2007 Abstract: The harmonic index of a graph G is defined as the sum of the weights \frac{2}{d(u)+d(v)} of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we present the minimum harmonic index for unicyclic graphs with given diameter and characterize the corresponding extremal graphs. This answers an unsolved problem of Zhu and Chang \cite{ZC14}. Keywords: harmonic index, unicyclic graphs, diameter Links: PDF