Some Properties of the Balanced Hypercube

Abstract

As a variant of [Formula: see text], Huang and Wu in [IEEE Transactions on Computers 46 (1997) 484–490] introduced the balanced hypercube [Formula: see text] as an interconnection network topology for computing systems. In this paper, we show that [Formula: see text] is a lexicographic product of two graphs, and using this, we show that every minimum cyclic vertex-cut of [Formula: see text] isolates a 4-cycle, and prove that the edge neighbor connectivity of [Formula: see text] is [Formula: see text].