LAUSR

The varietal hypercube graph $$VQ_n$$VQn ($$n\ge 1$$n≥1) was proposed by Cheng and Chuang (Varietal hypercube—a new interconnection network topology for large scale multicomputer, Proceedings of the International Conference on Parallel and Distributed Systems, pp 703–708, 1994) as a topology for interconnection network that is an improvement over the well-known hypercube network. It was known that $$VQ_n$$VQn is a Cayley graph on the group $$D_4^s\times {{\mathbb {Z}}}_2^t$$D4s×Z2t, where $$n=3s+t$$n=3s+t with $$s\ge 0$$s≥0 and $$0\le t\le 2$$0≤t≤2. In the present paper, we prove that the full automorphism group of the varietal hypercube graph $$VQ_n$$VQn is $$(D_4^s\times {{\mathbb {Z}}}_2^t) \rtimes (({\mathbb {Z}}_{2}\wr S_s)\times S_t)$$(D4s×Z2t)⋊((Z2≀Ss)×St). An open problem in the literature is to determine whether a given Cayley graph is normal and the result shows that the varietal hypercube graph $$VQ_n$$VQn is a normal Cayley graph on the group $$D_4^s\times {{\mathbb {Z}}}_2^t$$D4s×Z2t.