|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||Volume:||70||First page:||1281||Last page:||1290||Issue Date:||2022||Rank:||M21||ISSN:||0308-1087||DOI:||10.1080/03081087.2020.1758609||Abstract:||
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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