On graphs with adjacency and signless Laplacian matrix eigenvectors entries in $\{-1, +1\}$

Jorge Alencar; Leonardo de Lima

On graphs with adjacency and signless Laplacian matrix eigenvectors entries in $\{-1, +1\}$

Spectral Theory 2019-09-27 v1 Combinatorics

Authors: Jorge Alencar , Leonardo de Lima

Abstract

Let $G$ be a simple graph. In 1986, Herbert Wilf asked what kind of graphs have an eigenvector with entries formed only by $\pm 1$ ? In this paper, we answer this question for the adjacency, Laplacian and signless Laplacian matrix of a graph. Besides, we generalize the concept of an exact graph to the adjacency and signless Laplacian matrices. Infinity families of exact graphs for all those matrices are presented.

Keywords

simple graph adjacency matrix laplacian matrix signless laplacian matrix eigenvector exact graph wilf question

Cite

@article{arxiv.1909.11860,
  title  = {On graphs with adjacency and signless Laplacian matrix eigenvectors entries in $\{-1, +1\}$},
  author = {Jorge Alencar and Leonardo de Lima},
  journal= {arXiv preprint arXiv:1909.11860},
  year   = {2019}
}

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