Bipartite Representation of a Hypercube with Respect to the Norm of a Vertex

Abstract

Given a n-dimensional hypercube Q_n, we form a bipartite structure of Q_n with respect to norm of a vertex. The norm of a vertex is the number of ones in its binary representation. We prove some theorems which are useful to form the structure of a bipartite hypercube with respect to norm of a vertex. Also the circumference of Q_n is 2ⁿ.