The Wiener Index of Unicyclic Graphs with Girth and the Matching Number
  In this paper, we investigate how the Wiener index of unicyclic graphs varies with graph operations. These results are used to present a sharp lower bound for the Wiener index of unicyclic graphs of order $n$ with girth and the matching number $\beta\ge \frac{3g}{2}$. Moreover, we characterize all extremal graphs which attain the lower bound. 
Ya-Hong Chen and Xiao-Dong Zhang
math.CO