On the Harmonic Index of Triangle-Free Graphs

DOI: 10.4236/am.2013.48161   PDF   HTML     3,008 Downloads   4,616 Views   Citations

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.


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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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