On distance-regular Cayley graphs of generalized dicyclic groups

Abstract

Let G be a generalized dicyclic group with identity 1. An inverse closed subset S of G \ {1} is called minimal if S = G and there exists some s ∈ S such that S \ {s, s −1 } = G. In this paper, we characterize all distance-regular Cayley graphs Cay(G, S) of G under the condition that S is minimal.

Distance-regular Cayley graphs over dicyclic groups

“…Now suppose that z ∈ pZ 2n . Then (10) implies that if t = 0 then r(z) = λ−µ 2 and |t(z)| = δ, and that if t = 0 then r(z) ∈ {θ 1 , θ 3 }, where δ, θ 1 and θ 3 are given in (9).…”

“…Naturally, we propose the following problem. In [10], the authors determined all distance-regular Cayley graphs on generalized dicyclic groups under the condition that the connection set is minimal with respect to some element, and pointed out that complete graphs are the only primitive distance-regular Cayley graphs on generalized dicyclic groups.…”

“…10. ( [16,Lemma 3.4]) Let r be a positive divisor of n, and let A be a transversal of the subgrouprZ n in Z n .…”