On The Harmonic Index and The Girth for Graphs
نویسنده
چکیده
The harmonic index of a graph G is defined as the sum of the weights 2 d(u) + d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this work, we present the minimum and maximum values of the harmonic index for connected graphs with girth at least k (k ≥ 3), and characterize the corresponding extremal graphs. Using this result, we obtain several relations between the harmonic index and the girth of a graph.
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تاریخ انتشار 2014