Cycles in folded hypercubes

Cycles in folded hypercubes

This work investigates important properties related to cycles of embedding into the folded hypercube FQn for n ≥ 2. The authors observe that FQn is bipartite if and only if n is odd, and show that the minimum length of odd cycles is n + 1 if n is even. The authors further show that every edge of FQn lies on a cycle of every even length from 4 to 2n; if n is even, every edge of FQn also lies on ...

Fault-Free Cycles in Conditional Faulty Folded Hypercubes

An n-dimensional folded hypercube FQn is an attractive variance of an n-dimensional hypercube Qn, which is obtained by a standard hypercube with some extra edges established between its vertices. FQn for any odd n is known to be bipartite. In this paper, for any FQn (n ≥ 2) with at most 2n−3 faulty edges in which each vertex is incident with at least two fault-free edges, we prove that there ex...

1-vertex-fault-tolerant Cycles Embedding on Folded Hypercubes

In this paper, we focus on a hypercube-like structure, the folded hypercube, which is basically a standard hypercube with some extra links between its nodes. Let f be a faulty vertex in an n-dimensional folded hypercube FQn. We show that FQn−{f } contains a faultfree cycle of every even length from 4 to 2n−2 if n ≥ 3 and, furthermore, every odd length from n+ 1 to 2n − 1 if n ≥ 2 and n is even....

Cycles in enhanced hypercubes

The enhanced hypercube Qn,k is a variant of the hypercube Qn. We investigate all the lengths of cycles that an edge of the enhanced hypercube lies on. It is proved that every edge of Qn,k lies on a cycle of every even length from 4 to 2; if k is even, every edge of Qn,k also lies on a cycle of every odd length from k+3 to 2 − 1, and some special edges lie on a shortest odd cycle of length k + 1.

Edge-fault-tolerant properties of hypercubes and folded hypercubes