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On the Harmonic Index of Triangle-Free Graphs
Department of Applied Mathematics, School of Informatics, Guangdong University of Foreign Studies, Guangzhou, China
- 1 Department of Applied Mathematics, School of Informatics, Guangdong University of Foreign Studies, Guangzhou, China
Applied Mathematics·Volume 04 (2013)·Pages 1204–1206·Published 23 July 2013·DOI10.4236/am.2013.48161
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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 k ≤ n /2 and show the corresponding extremal graph is the complete graph .
KeywordsHarmonic IndexMinimum DegreeTriangle-Free
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