T-COLORING ON 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 ...

On conditional diagnosability of the folded hypercubes

The n-dimensional folded hypercube FQn, a variation of the hypercube proposed by Ahmed et al. [A. El-Amawy, S. Latifi, Properties and performance of folded hypercubes, IEEE Transactions on Parallel and Distributed Systems 2(3) (1991) 31–42], is an (n + 1)-regular (n + 1)-connected graph. Conditional diagnosability, a new measure of diagnosability introduced by Lai et al. [Pao-Lien Lai, Jimmy J....

On reliability of the folded hypercubes q

In this paper, we explore the 2-extra connectivity and 2-extra-edge-connectivity of the folded hypercube FQn. We show that j2(FQn) = 3n 2 for n P 8; and k2(FQn) = 3n 1 for n P 5. That is, for n P 8 (resp. n P 5), at least 3n 2 vertices (resp. 3n 1 edges) of FQn are removed to get a disconnected graph that contains no isolated vertices (resp. edges). When the folded hypercube is used to model th...

Edge-fault-tolerant properties of hypercubes and folded hypercubes

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.