On the Harmonic Index of Triangle-Free Graphs

Jianxi Liu

Department of Applied Mathematics, School of Informatics, Guangdong University of Foreign Studies, Guangzhou, China.

DOI: 10.4236/am.2013.48161                

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 k≤ n/2  and show the corresponding extremal graph is the complete graph.

Keywords

Harmonic Index; Minimum Degree; Triangle-Free

Conflicts of Interest

The authors declare no conflicts of interest.

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