On the second largest eigenvalue of the signless Laplacian

10Citations
Citations of this article
9Readers
Mendeley users who have this article in their library.

Abstract

Let G be a graph of order n, and let q1(G)≥⋯≥q n(G) be the eigenvalues of the Q-matrix of G, also known as the signless Laplacian of G. We give a necessary and sufficient condition for the equality qk(G)=n-2, where 1<k≤n. In particular, this result solves an open problem raised by Wang, Belardo, Huang and Borovicanin. We also show thatq2(G)≥δ(G)and determine all graphs for which equality holds. © 2012 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

De Lima, L. S., & Nikiforov, V. (2013). On the second largest eigenvalue of the signless Laplacian. Linear Algebra and Its Applications, 438(3), 1215–1222. https://doi.org/10.1016/j.laa.2012.07.052

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free