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On the eigenvalues of signed complete graphs

Akbari, S ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1080/03081087.2017.1403548
  3. Publisher: Taylor and Francis Ltd , 2019
  4. Abstract:
  5. Let (Formula presented.) be a signed graph, where G is the underlying simple graph and (Formula presented.) is the sign function on the edges of G. The adjacency matrix of a signed graph has (Formula presented.) or (Formula presented.) for adjacent vertices, depending on the sign of the connecting edges. In this paper, the eigenvalues of signed complete graphs are investigated. We prove that (Formula presented.) and 1 are the eigenvalues of the signed complete graph with the multiplicity at least t if there are (Formula presented.) vertices whose all incident edges are positive or negative, respectively. We study the spectrum of a signed complete graph whose negative edges induce an r-regular subgraph H. We obtain a relation between the eigenvalues of this signed complete graph and the eigenvalues of H. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group
  6. Keywords:
  7. Adjacency matrix ; Complete graph ; Signed graph
  8. Source: Linear and Multilinear Algebra ; Volume 67, Issue 3 , 2019 , Pages 433-441 ; 03081087 (ISSN)
  9. URL: https://www.tandfonline.com/doi/abs/10.1080/03081087.2017.1403548?journalCode=glma20