A Nordhaus-Gaddum type problem for the normalized Laplacian spectrum and graph Cheeger constant

J. Nolan Faught, Mark Kempton and Adam Knudson

Applied Mathematics and Computation, 2024, vol. 480, issue C

Abstract: For a graph G on n vertices with normalized Laplacian eigenvalues 0=λ1(G)≤λ2(G)≤⋯≤λn(G) and graph complement Gc, we prove thatmax⁡{λ2(G),λ2(Gc)}≥2n2. We do this by way of lower bounding max⁡{i(G),i(Gc)} and max⁡{h(G),h(Gc)} where i(G) and h(G) denote the isoperimetric number and Cheeger constant of G, respectively.

Keywords: Normalized Laplacian; Nordhaus-Gaddum problems; Laplacian spread; Algebraic connectivity; Isoperimetric number; Cheeger constant (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324003813
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:480:y:2024:i:c:s0096300324003813

DOI: 10.1016/j.amc.2024.128920

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().