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

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