The harmonic index of unicyclic graphs.

The harmonic index of a graph , denoted by , is defined as the sum of weights over all edges of , where denotes the degree of a vertex . Hu and Zhou [ WSEAS Trans. Math. 12 (2013) 716-726] proved that for any unicyclic graph of order , with equality if and only if . Recently, Zhong and Cui [ Filomat 29 (2015) 673-686] generalized the above bound and proved that for any unicyclic graph of order other than , . In this paper, we generalize the aforemention results and show that for any connected unicyclic graph of order with maximum degree , and classify the extremal unicyclic graphs. [ABSTRACT FROM AUTHOR]