The harmonic index for bicyclic graphs - Zhong, Lingping; Xu, Kexiang (Utilitas Mathematica, 2013)
The harmonic index H(G)of a graph G is defined as the sum of 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' paper,we have determined the minimum and maximum harmonic indices of bicyclic graphs and characterized the corresponding graphs at which the extremal harmonic indices are attained.