on the harmonic index of bicyclic graphs

The harmonic index of a graph g, denoted by h(g), is defined as thesum of weights 2/[d(u) + d(v)] over all edges uv of g, where d(u) denotes the degree of a vertex u. hu and zhou [y. hu and x. zhou, wseas trans. math. 12 (2013)716–726] proved that for any bicyclic graph g of order n ≥ 4, h(g) ≤ ⁿ − ¹ and2 15characterized all extremal bicyclic graphs. in this paper, we prove that for any bicyclicgraph g of order n ≥ 4 and maximum degree ∆, and characterize all extremal bicyclic graphs.