Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897861 | Linear Algebra and its Applications | 2018 | 11 Pages |
Abstract
By the well-known Perron-Frobenius Theorem [3], for a connected graph G, its largest eigenvalue strictly increases when an edge is added. We are interested in how the other eigenvalues of a connected graph change when edges are added. Examples show that all cases are possible: increased, decreased, unchanged. In this paper, we consider the effect on the eigenvalues by suitably adding edges in particular families, say the family of connected graphs with clusters. By using the result, we also consider the effect on the energy by suitably adding edges to the graphs of the above families.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ji-Ming Guo, Pan-Pan Tong, Jianxi Li, Wai Chee Shiu, Zhi-Wen Wang,