Spectra of strongly Deza graphs

Saieed Akbari, Willem H. Haemers, Mohammad Ali Hosseinzadeh, Vladislav V. Kabanov, Elena V. Konstantinova*, Leonid Shalaginov

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


A Deza graph G with parameters (n,k,b,a) is a k-regular graph with n vertices such that any two distinct vertices have b or a common neighbours. The children GA and GB of a Deza graph G are defined on the vertex set of G such that every two distinct vertices are adjacent in GA or GB if and only if they have a or b common neighbours, respectively. A strongly Deza graph is a Deza graph with strongly regular children. In this paper we give a spectral characterisation of strongly Deza graphs, show relationships between eigenvalues, and study strongly Deza graphs which are distance-regular.
Original languageEnglish
Article number112622
JournalDiscrete Mathematics
Issue number12
Publication statusPublished - Dec 2021


  • Cospectral graphs
  • Deza graph
  • Distance-regular graph
  • Divisible design graph
  • Eigenvalues
  • Strongly regular graph


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