Volume 36 • Number 3 • 2013   • Extremal Bicyclic Graph with Perfect Matching for Different Indices Shan Duan and Zhongxun Zhu Abstract. Let $\mathscr{B}(2m,m)$ be the set of all bicyclic graphs on $2m(m\geq 2)$ vertices with perfect matchings. In this paper, we characterize the bicyclic graphs with minimal number of matchings and maximal number of independent sets in $\mathscr{B}(2m,m)$. 2010 Mathematics Subject Classification: 49M15, 65K10 Full text: PDF