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

Jorge Alencar; Leonardo de Lima

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arXiv · 1909.11860

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

Jorge Alencar·Leonardo de Lima

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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.

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Jorge Alencar, Leonardo de Lima. 2019-09-26. On graphs with adjacency and signless Laplacian matrix eigenvectors entries in $\{-1, +1\}$. https://arxiv.org/abs/1909.11860

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