Subdivision and Graph Eigenvalues
Combinatorics
2023-03-21 v1
Abstract
This paper investigates the asymptotic nature of graph spectra when some edges of a graph are subdivided sufficiently many times. In the special case where all edges of a graph are subdivided, we find the exact limits of the -th largest and -th smallest eigenvalues for any fixed . It is expected that after subdivision, most eigenvalues of the new graph will lie in the interval . We examine the eigenvalues of the new graph outside this interval, and we prove several results that might be of independent interest.
Cite
@article{arxiv.2303.10488,
title = {Subdivision and Graph Eigenvalues},
author = {Hitesh Kumar and Bojan Mohar and Shivaramakrishna Pragada and Hanmeng Zhan},
journal= {arXiv preprint arXiv:2303.10488},
year = {2023}
}