A structural property of enhanced hypercube
Dan Yuan, Hongmei Liu · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2015
This work investigates the important properties related to adjacent structure of enhanced hypercube Qn,k . It is observed that for any two vertices u, v in, Qn,k (2 ≤ k ≤ n − 1, k ≠ n − 2) , if the distance d(u, v) = 2 , then there exactly exist two paths of length 2 joining u and v for n ≥ 5 . In other words, if u and v have a common neighbor, they exactly share two common neighbors. The result is very important to its diagnosability.