Authors: Cheng, Tao
Feng, Lihua
Liu, Weijun
Lu, Lu
Stevanović, Dragan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Distance powers of integral Cayley graphs over dihedral groups and dicyclic groups
Journal: Linear and Multilinear Algebra
Issue Date: 27-Apr-2020
Rank: M21
ISSN: 0308-1087
DOI: 10.1080/03081087.2020.1758609
In this paper, we focus on the dihedral groups and the dicyclic groups, and consider their corresponding integral Cayley graphs. We obtain the sufficient conditions for the integrality of the distance powers ᴦD of the Cayley graph ᴦ = X(D2n, S) (resp. ᴦ = X(D4n, S)) (n ≥ 3)) for a set of nonnegative integers D. In particular, for a prime p, we show that if ᴦ = X(D2p, S) (resp. ᴦ = X(D4p, S)) is integral, then the distance powers of ᴦ = X(D2p, S) (resp. ᴦ = X(D4p, S)) are integral Cayley graphs.
Keywords: 05C25 | 05C50 | dicyclic groups | dihedral groups | Distance powers | integral Cayley graph
Publisher: Taylor & Francis

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