How many triangles and quadrilaterals are there in an n-dimensional augmented cube?

Abstract

The augmented cube is an important variant of hypercube as interconnection topology of parallel computing. In this paper, we examine the numbers of short cycles in augmented cubes, and prove that for n≥3, there are 2n×(n−1) triangles and 2n−2×(2n2+5n−11) quadrilaterals in an n-dimensional augmented cube. This result shows that augmented cubes are promising interconnection networks with superior connectivity and fault-tolerant capability.