THE HARMONIC INDEX FOR UNICYCLIC AND BICYCLIC GRAPHS WITH GIVEN MATCHING NUMBER.

The harmonic index of a graph G is defined as the sum of the weights 2/d(u)+d(u) 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 ≤ [n/2]), respectively. The corresponding extremal graphs are also characterized. [ABSTRACT FROM AUTHOR]