17 Embedding of Simple Cycles in Hypercubes

Cycle embedding is an important issue in interconnection networks. Embedding cycles of different sizes into a network are beneficial to the efficient execution of parallel programs. The hypercube is a popular network because of its attractive properties. Given an n-dimensional hypercube $Qn$ and let e be any edge of $Qn$. In this paper, we discuss the number of simple k-cycles in $Qn$, which pass through the edge e for $k=4,6,and8$.