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Nowhere-zero eigenvectors of graphs

Akbari, S ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1080/03081087.2012.675331
  3. Publisher: 2013
  4. Abstract:
  5. A vector is called nowhere-zero if it has no zero entry. In this article we search for graphs with nowhere-zero eigenvectors. We prove that distance-regular graphs and vertex-transitive graphs have nowhere-zero eigenvectors for all of their eigenvalues and edge-transitive graphs have nowhere-zero eigenvectors for all non-zero eigenvalues. Among other results, it is shown that a graph with three distinct eigenvalues has a nowhere-zero eigenvector for its smallest eigenvalue
  6. Keywords:
  8. Source: Linear and Multilinear Algebra ; Volume 61, Issue 2 , 2013 , Pages 273-279 ; 03081087 (ISSN)
  9. URL: http://www.tandfonline.com/doi/abs/10.1080/03081087.2012.675331#.VlGUxC6Hi-E