The vulnerability of the diameter of folded n-cubes

The vulnerability of the diameter of the enhanced hypercubes

“…The special case k = n (folded hypercube) was obtain earlier by Simó and Yebra [19], along with the same values for edge deletions. For enhanced hypercubes also, our arguments yield the same values for edge deletions as for vertex deletions.…”

“…These parameters were studied by several authors for some Cartesian product graphs [7,25,26] and for the hypercube and its variants [3,5,8,10,18,19,20].…”

The spanning connectivity of folded hypercubes☆

“…There are n + 1 internally disjoint paths of length at most n 2 AE Ç þ 1 between any pair of vertices in FQ n , the deletion of less than n 2 AE Ç À 2 vertices or edges does not increase the diameter of FQ n [13,24]. Thus, the folded hypercube FQ n is an enhancement on the hypercube Q n .…”

Some results on topological properties of folded hypercubes

“…,n. The n-dimensional folded hypercube FQ n is superior to the n-cube Q n in some properties. For example, its diameter is n 2 , about half the diameter of Q n [5]; there are n + 1 internally disjoint paths of length at most n 2 + 1 between any pair of vertices [19]; there exists a cycle of every length l with n + 1 l 2 n − 1 if n is even [24]. Many results on folded hypercubes can be found in papers [3,5,6,8,9,11,12,19,[24][25][26].…”