AM  Vol.4 No.8 , August 2013
On the Harmonic Index of Triangle-Free Graphs
Author(s) Jianxi Liu
ABSTRACT

The harmonic index of a graph G  is defined as where d(u) denotes the degree of a vertex u in G . In this work, we give another expression for the Harmonic index. Using this expression, we give the minimum value of the harmonic index for any triangle-free graphs with order n and minimum degree δ k for kn/2  and show the corresponding extremal graph is the complete graph.



Cite this paper
J. Liu, "On the Harmonic Index of Triangle-Free Graphs," Applied Mathematics, Vol. 4 No. 8, 2013, pp. 1204-1206. doi: 10.4236/am.2013.48161.
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