Some complete cycles on the š¯‘›-cube
William Hobson Mills Ā· Proceedings of the American Mathematical Society Ā· 1963
1. Let Q * be the n-dimensional hypercube (or n-cube) whose vertices are the 2n vectors of dimension n with components 0's and l's. Let Qn be the graph that consists of the edges and vertices of Q,,*. A complete cycle (or Hamilton circuit) on Qn is a cyclic path on the graph Qn that passes through each vertex once and onlly once. Let C be such a cycle and let P1, P2, * * *, P2n=Po be the consecutive vertices of C. Any two consecutive vertices Pi, Pi+, differ in exactly one component. Let Ai denote the index of that component. Then A is called the ith change number of C. The subscripts i in the Pi and the Ai are taken modulo 2 . Clearly C is determined by P1 and tlle sequence of 2n change numbers