Open AccessThe minimum harmonic index for unicyclic graphs with given diameter
Author(s) -
Lingping Zhong
Publication year - 2017
Publication title -
discussiones mathematicae graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.476
H-Index - 19
eISSN - 2083-5892
pISSN - 1234-3099
DOI - 10.7151/dmgt.2007
Subject(s) - mathematics , combinatorics , index (typography) , discrete mathematics , computer science , world wide web
The harmonic index of a graph G is defined as the sum of the weights 2d(u)+d(v) ${2 \over {d(u) + d(v)}}$ 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 [26].
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