The Reciprocal Reverse Wiener Index of Unicyclic Graphs

Jianping Li, Bo Zhou

The reciprocal reverse Wiener index $R\Lambda(G)$ of a connected graph $G$ is defined in mathematical chemistry as the sum of weights $\frac1{d(G)-d_G(u,v)}$ of all unordered pairs of distinct vertices $u$ and $v$ with $d_G(u,v)<d(G)$, where $d_G(u,v)$ is the distance between vertices $u$ and $v$ in $G$ and $d(G)$ is the diameter of $G$. We determine the minimum and maximum reciprocal reverse Wiener indices in the class of $n$-vertex unicyclic graphs and characterize the corresponding extremal graphs.