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 rad...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.展开更多
Based on some recent results for interlacing eigenvalue intervals from 1-parameter families of se- quences of eigenvalue inequalities, a new method is given to solving the index problem for Sturm-Liouville eigenvalues...Based on some recent results for interlacing eigenvalue intervals from 1-parameter families of se- quences of eigenvalue inequalities, a new method is given to solving the index problem for Sturm-Liouville eigenvalues for coupled self-adjoint boundary conditions in the regular case. The key is a new characteristic principle for indices for Sturm-Liouville eigenvalues. The algorithm corresponding on the characteristic princi- ple are discussed, and numerical examples are presented to illustrate the theoretical results and show that the algorithm is valid.展开更多
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.
文摘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Supported by the National Natural Science Foundation of China(No.11361039 and 11161030)the Natural Science Foundation of Inner Mongolia Province,China(No.2013MS0116)
文摘Based on some recent results for interlacing eigenvalue intervals from 1-parameter families of se- quences of eigenvalue inequalities, a new method is given to solving the index problem for Sturm-Liouville eigenvalues for coupled self-adjoint boundary conditions in the regular case. The key is a new characteristic principle for indices for Sturm-Liouville eigenvalues. The algorithm corresponding on the characteristic princi- ple are discussed, and numerical examples are presented to illustrate the theoretical results and show that the algorithm is valid.
