## Abstract

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 C_{Σ}(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 language | English |
---|---|

Article number | 102272 |

Journal | Advances in Applied Mathematics |

Volume | 132 |

DOIs | |

State | Published - 1 Jan 2022 |

Externally published | Yes |

## Keywords

- 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