Automorphism group of the balanced hypercube

Abstract

Huang and Wu in [IEEE Transactions on Computers 46 (1997), pp. 484–490] introduced the balanced hypercube BH_n as an interconnection network topology for computing systems. In this paper, we completely determine the full automorphism group of the balanced hypercube. Applying this, we first show that the n-dimensional balanced hypercube BH_n is arc-transitive but not 2-arc-transitive whenever n ≥ 2. Then, we show that BH_n is a lexicographic product of an n-valent graph X_n and the null graph with two vertices, where X_n is a Z₂^n − 1-regular cover of the n-dimensional hypercube Q_n.