The Sharp Lower Bound of the Least Eigenvalue of a Bicyclic Graph

Shu-Guang Guo 1, 2
1 Department of Mathematics, Southeast University, Nanjing 210096, P. R. China
2 Department of Mathematics, Yancheng Teachers College, Yancheng 224002, P. R. China


Abstract     Full Text  PDF

Bicyclic graphs are connected graphs in which the number of edges equals the number of vertices plus one. In this paper we determine the first three graphs among all bicyclic graphs with $n$ vertices, ordered according to their least eigenvalues in increasing order.