On graphs with eigenvectors in $\{1, -1, 0\}$ and the max $k$-cut problem
Combinatorics
2022-11-29 v1 Spectral Theory
Abstract
In this paper, we characterize all graphs with eigenvectors of the signless Laplacian and adjacency matrices with components equal to We extend the graph parameter max -cut to square matrices and prove a general sharp upper bound, which implies upper bounds on the max -cut of a graph using the smallest signless Laplacian eigenvalue, the smallest adjacency eigenvalue, and the largest Laplacian eigenvalue of the graph. In addition, we construct infinite families of extremal graphs for the obtained upper bounds.
Cite
@article{arxiv.2211.15314,
title = {On graphs with eigenvectors in $\{1, -1, 0\}$ and the max $k$-cut problem},
author = {Jorge Alencar and Leonardo de Lima and Vladimir Nikiforov},
journal= {arXiv preprint arXiv:2211.15314},
year = {2022}
}