On the Harmonic Index of Triangle-Free Graphs ()
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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.
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