CYCLE AND PATH EMBEDDING ON 5-ARY N-CUBES

We st u d y two t op ological p rop e rt ies of t h e 5- aryn-cub eQ5n. Given two arbitrary distinct no des x an d y in Q5n,weprovethatthere exists an x - y p at h of every len gt h r an gin g from 2n to 5n− 1, wh eren ≥ 2. Based on this result, we prove that Q5nis 5- ed ge- p an cy clic bysh owin g t h at e ve ry ed ge in Q5nlies on a cy cle of e ve ry len gt h ran gin gfrom 5to5n