Automorphism group of the balanced hypercube - Zhou, Jin-Xin (Ars mathematica contemporanea, 2017)
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 ?$n \ge 2$?. 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 ?$\mathbb{Z}^{n-1}_2$?-regular cover of the ?$n$?-dimensional hypercube ?$Q_n$?.
Keywords: Cayleyjev graf; grafi; grupa avtomorfizmov; uravnotežena hiperkocka