Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4601830 | Linear Algebra and its Applications | 2010 | 14 Pages |
Abstract
Let G be a graph with n vertices and μ(G) be the largest eigenvalue of the adjacency matrix of G. We study how large μ(G) can be when G does not contain cycles and paths of specified order. In particular, we determine the maximum spectral radius of graphs without paths of given length, and give tight bounds on the spectral radius of graphs without given even cycles. We also raise a number of open problems.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory