摘要
The Method of Eigenvalue Interlacing for Graphs is used to investigate some problems on graphs, such as the lower bounds for the spectral radius of graphs. In this paper, two new sharp lower bounds on the spectral radius of graphs are obtained, and a relation between the Laplacian spectral radius of a graph and the number of quadrangles in the graph is deduced.
The Method of Eigenvalue Interlacing for Graphs is used to investigate some problems on graphs, such as the lower bounds for the spectral radius of graphs. In this paper, two new sharp lower bounds on the spectral radius of graphs are obtained, and a relation between the Laplacian spectral radius of a graph and the number of quadrangles in the graph is deduced.
基金
Foundation item： the National Natural Science Foundation of China （No. 10431020）
the Natural Science Foundation of Fujian Province （No. Z0511016）.Acknowledgements The authors would like to thank referees for their comments and careful reading of the original paper which greatly improve the clarity of this paper.
