MMN-1033
The harmonic index for unicyclic and bicyclic graphs with given matching number
Abstract
The harmonic index of a graph $G$ is defined as the sum of the weights $\frac{2}{d(u)+d(v)}$ of all edges $uv$ of $G$, where $d(u)$ denotes the degree of a vertex $u$ in $G$. In this paper, we present the minimum harmonic indices for unicyclic and bicyclic graphs with $n$ vertices and matching number $m$ ($2\leq m\leq\lfloor\frac{n}{2}\rfloor$), respectively. The corresponding extremal graphs are also characterized.
Vol. 16 (2015), No. 1, pp. 587-605