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On the Harmonic Index of Triangle-Free Graphs

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DOI: 10.4236/am.2013.48161    2,885 Downloads   4,453 Views   Citations
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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.


Conflicts of Interest

The authors declare no conflicts of interest.

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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