Department of Mathematics
By the well-known Perron–Frobenius Theorem , 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.
Graph, Eigenvalue, Adding an edge, Energy
Source Publication Title
Linear Algebra and its Applications
© 2018 Elsevier Inc. All rights reserved.
Partially supported by NSF of China(No.11371372); Program for New Century Ex- cellent Talents in Fujian Province University; Project of Fujian Education Department (No.JZ160455); Research Fund of Minnan Normal University (No.MX1603).
Link to Publisher's Edition
Guo, J., Tong, P., Li, J., Shiu, W., & Wang, Z. (2018). The effect on eigenvalues of connected graphs by adding edges. Linear Algebra and its Applications, 548, 57-65. https://doi.org/10.1016/j.laa.2018.02.012
Available for download on Saturday, August 01, 2020