Partial characterization of graphs having a single large Laplacian eigenvalue
Combinatorics
2017-10-05 v1
Abstract
The parameter of a graph stands for the number of Laplacian eigenvalues greater than or equal to the average degree of . In this work, we address the problem of characterizing those graphs having . Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between and the number of anticomponents of . As a by-product, we present some results which support the conjecture, by restricting our analysis to some classes of graphs.
Cite
@article{arxiv.1710.01710,
title = {Partial characterization of graphs having a single large Laplacian eigenvalue},
author = {L. Emilio Allem and Antonio Cafure and Ezequiel Dratman and Luciano N. Grippo and Martín D. Safe and Vilmar Trevisan},
journal= {arXiv preprint arXiv:1710.01710},
year = {2017}
}
Comments
10 pages