On the Spectral Radii of Bicyclic Graphs
Received:March 20, 2006  Revised:January 17, 2007
Key Word: bicyclic graph   spectral radius   characteristic polynomial.
Fund ProjectL:the National Natural Science Foundation of China (10331020).
 Author Name Affiliation HE Chang-xiang Department of Mathematics, Tongji University, Shanghai 200092, China LIU Yue Department of Mathematics, Tongji University, Shanghai 200092, China SHAO Jia-yu Department of Mathematics, Tongji University, Shanghai 200092, China
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A graph $G$ of order $n$ is called a bicyclic graph if $G$ is connected and the number of edges of $G$ is $n+1$. Let ${\cal B}(n)$ be the set of all bicyclic graphs on $n$ vertices. In this paper, the first three largest spectral radii in the class ${\cal B}(n)$~($n\geq 9$) together with the corresponding graphs are given.