Integral graphs obtained by dual Seidel switching

Sergey Goryainov, Elena V. Konstantinova, Honghai Li, Da Zhao

Research output: Contribution to journalArticlepeer-review


Dual Seidel switching is a graph operation introduced by W. Haemers in 1984. This operation can change the graph, however it does not change its bipartite double, and because of this, the operation leaves the squares of the eigenvalues invariant. Thus, if a graph is integral then it is still integral after dual Seidel switching. In this paper two new infinite families of integral graphs are obtained by applying dual Seidel switching to the Star graphs and the Odd graphs. In particular, three new 4-regular integral graphs with their spectra are found.

Original languageEnglish
Pages (from-to)476-489
Number of pages14
JournalLinear Algebra and Its Applications
Publication statusPublished - 1 Nov 2020


  • 4-Regular graph
  • Dual Seidel switching
  • Integral graph
  • Multiple Kronecker covering
  • Odd graph
  • Star graph

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