Spectra of twists of Cayley and Cayley sum graphs

Arindam Biswas, Jyoti Prakash Saha

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Let G be a finite group with |G|≥4 and S be a subset of G. Given an automorphism σ of G, the twisted Cayley graph C(G,S)σ is the graph with G as its set of vertices, and the neighbourhood of a vertex is obtained by applying σ to its neighbourhood in the Cayley graph of G with respect to S. If C(G,S)σ is undirected and connected, then we prove that the nontrivial spectrum of its normalised adjacency operator is bounded away from −1 and this bound depends only on its degree, the order of σ and the vertex Cheeger constant of C(G,S)σ. The twisted Cayley sum graph CΣ(G,S)σ is defined similarly and we establish an analogous result for it. Further, we prove an analogous result for the Schreier graphs satisfying certain conditions.

Original languageEnglish
Article number102272
JournalAdvances in Applied Mathematics
StatePublished - 1 Jan 2022
Externally publishedYes


  • Cheeger inequality
  • Expander graphs
  • Spectra of generalised Cayley graphs
  • Spectra of twists of Cayley graphs
  • Spectra of twists of Cayley sum graphs
  • Twists by automorphisms

ASJC Scopus subject areas

  • Applied Mathematics


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