Distance powers of integral Cayley graphs over dihedral groups and dicyclic groups

Tao Cheng, Lihua Feng, Weijun Liu, Lu Lu(鲁卢), Dragan Stevanovic

July 2020

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 D of the Cayley graph = X(D2n, S) (resp. = X(T4n, S)) (n ≥ 3) for a set of nonnegative integers D. In particular, for a prime p, we show that if = X(D2p, S) (resp. = X(T4p, S)) is integral, then the distance powers of = X(D2p, S) (resp. = X(T4p, S)) are integral Cayley graphs.

Publication

In Linear and Multilinear Algebra

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Distance powers of integral Cayley graphs over dihedral groups and dicyclic groups

Abstract

Lu Lu(鲁卢)

Associate Professor, PhD Supervisor