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Spectra of Deza graphs

Akbari, S ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1080/03081087.2020.1723472
  3. Publisher: Taylor and Francis Ltd , 2020
  4. Abstract:
  5. A Deza graph with parameters (n, k, b, a) is a k-regular graph with n vertices such that any two of its vertices have b or a common neighbours, where b ≥ a. In this paper we investigate spectra of Deza graphs. In particular, using the eigenvalues of a Deza graph we determine the eigenvalues of its children. Divisible design graphs are significant cases of Deza graphs. Sufficient conditions for Deza graphs to be divisible design graphs are given, a few families of divisible design graphs are presented and their properties are studied. Our special attention goes to the invertibility of the adjacency matrices of Deza graphs. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group
  6. Keywords:
  7. Deza children ; Deza graph ; Divisible design graph ; Nullity ; Spectrum of graph
  8. Source: Linear and Multilinear Algebra ; 2020
  9. URL: https://www.tandfonline.com/doi/abs/10.1080/03081087.2020.1723472?journalCode=glma20