The Harmonic Index for Unicyclic and Bicyclic Graphs with given Matching Number
نویسنده
چکیده
The harmonic index of a graph G is defined as the sum of the weights 2 d.u/Cd.v/ of all edges uv of G, where d.u/ denotes the degree of a vertex u in G. In this paper, we present the minimum harmonic indices for unicyclic and bicyclic graphs with n vertices and matching number m (2 m bn2 c), respectively. The corresponding extremal graphs are also characterized. 2000 Mathematics Subject Classification: 05C07; 05C70; 05C35; 92E10
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