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A NOTE ON n-CAYLEY GRAPHS: EXPANDER FAMILIES AND GALOIS COVERINGS | Synapse

April 1, 2026Open Access

A NOTE ON n-CAYLEY GRAPHS: EXPANDER FAMILIES AND GALOIS COVERINGS

Key Points

The paper aims to explore the properties of n-Cayley graphs over groups, particularly their relationship with expander families and Galois coverings.
Show that a sequence of n-Cayley graphs over solvable groups cannot form an expander family.
Establish equivalence between connected n-Cayley graphs and Galois coverings with the corresponding Galois group.
Demonstrated that n-Cayley graphs over solvable groups cannot create an expander family.
Confirmed that being an n-Cayley graph is equivalent to being a Galois covering with Galois group G.

Abstract

A graph Γ is called an n-Cayley graph over a group G if there exists a semiregular subgroup of Aut(Γ) that is isomorphic to G with n orbits (of equal size). This is one of the generalizations of Cayley graphs. In this paper, we show that a sequence of n-Cayley graphs over solvable groups cannot form an expander family. We also show that a connected graph being an n-Cayley graph over G is equivalent to being a Galois covering with Galois group G.

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Cite This Study

Nao Toyama (Fri,) studied this question.

synapsesocial.com/papers/69cd7a4e5652765b073a7515 https://doi.org/https://doi.org/10.24564/0002021003

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