Properties of the Binary Hypercube and Middle Level Graphs

This paper takes a look at various properties of binary hypercubes and middle level graphs, a particular subgraph of the binary hypercube. The intention is to shed some light on the middle level conjecture by discovering patterns within the subgraphs and the known Hamiltonian cycles for those graphs. The problem is closely related to determining Hamiltonicity of graphs and is also closely tied to Gray code cycles and binary sequences.