Restricted Arc Connectivity of Unidirectional Hypercubes and Unidirectional Folded Hypercubes

Hamiltonian-connectivity and strongly Hamiltonian-laceability of folded hypercubes

In this paper, we analyze a hypercube-like structure, called the folded hypercube, which is basically a standard hypercube with some extra links established between its nodes. We first show that the n-dimensional folded hypercube is bipartite when n is odd.We also show that the n-dimensional folded hypercube is strongly Hamiltonian-laceable when n is odd, and is Hamiltonian-connected when n = 1...

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 ...

Edge-fault-tolerant properties of hypercubes and folded hypercubes

Hamiltonian-Connectivity and Related Property on Folded Hypercubes

In this paper, we analysis a hypercube-like structure, called the Folded Hypercube, which is basically a standard hypercube with some extra links established between its nodes. We first show that the n-dimensional folded hypercube is bipartite when n is odd. We also show that the n-dimensional folded hypercube is strongly Hamiltonian-laceable when n is odd, and is Hamiltonian-connected when n =...

Algebraic Properties and Panconnectivity of Folded Hypercubes

This paper considers the folded hypercube FQn, as an enhancement on the hypercube, and obtain some algebraic properties of FQn. Using these properties the authors show that for any two vertices x and y in FQn with distance d and any integers h ∈ {d, n + 1 − d} and l with h ≤ l ≤ 2 − 1, FQn contains an xy-path of length l and no xy-paths of other length provided that l and h have the same parity.