Automorphisms and isomorphisms of enhanced hypercubes

Lu Lu ; Qiongxiang Huang

Filomat, Tome 34 (2020) no. 8, p. 2805

Résumé

Let Z n 2 be the elementary abelian 2-group, which can be viewed as the vector space of dimension n over F 2. Let {e 1 ,. .. , e n } be the standard basis of Z n 2 and k = e k + · · · + e n for some 1 ≤ k ≤ n − 1. Denote by Γ n,k the Cayley graph over Z n 2 with generating set S k = {e 1 ,. .. , e n , k }, that is, Γ n,k = Cay(Z n 2 , S k). In this paper, we characterize the automorphism group of Γ n,k for 1 ≤ k ≤ n − 1 and determine all Cayley graphs over Z n 2 isomorphic to Γ n,k. Furthermore, we prove that for any Cayley graph Γ = Cay(Z n 2 , T), if Γ and Γ n,k share the same spectrum, then Γ Γ n,k. Note that Γ n,1 is known as the so called n-dimensional folded hypercube FQ n , and Γ n,k is known as the n-dimensional enhanced hypercube Q n,k.

Détail

DOI : 10.2298/FIL2008805L

Classification : 05C25, 05C60, 05C50
Keywords: enhanced hypercube, Cayley graphs, automorphism, isomorphism, spectrum