(n − 2)-Fault-Tolerant Edge-Pancyclicity of Crossed Cubes CQn

As one of the most fundamental networks for parallel and distributed computation, cycle is suitable for developing simple algorithms with low communication cost. A graph [Formula: see text] is called [Formula: see text]-fault-tolerant edge-pancyclic if after deleting any faulty set [Formula: see text] of [Formula: see text] vertices and/or edges from [Formula: see text], every correct edge in the resulting graph lies in a cycle of every length from [Formula: see text] to [Formula: see text], inclusively, where [Formula: see text] is the girth of [Formula: see text], the length of a shortest cycle in [Formula: see text]. The [Formula: see text]-dimensional crossed cube [Formula: see text] is an important variant of the hypercube [Formula: see text], which possesses some properties superior to the hypercube. This paper investigates the fault-tolerant edge-pancyclicity of [Formula: see text], and shows that if [Formula: see text] contains at most [Formula: see text] faulty vertices and/or edges then, for any fault-free edge [Formula: see text] and every length [Formula: see text] from [Formula: see text] to [Formula: see text] except [Formula: see text], there is a fault-free cycle of length [Formula: see text] containing the edge [Formula: see text]. The result is optimal in some senses.

The Conditional Reliability Evaluation of Data Center Network BCDC

As the number of servers in a data center network (DCN) increases, the probability of server failures is significantly increased. Traditional connectivity is an important metric to measure the reliability of DCN. However, the traditional connectivity of a DCN based on the condition of arbitrary faulty servers is generally lower. Therefore, it is important to increase the connectivity of a DCN by adding some limited conditions for the faulty server set. As a result, $g$-restricted connectivity and $h$-extra connectivity, which are two crucial subjects for a DCN’s ability to tolerate faulty servers, were proposed in the literature. In this paper, we study the $g$-restricted connectivity and $h$-extra connectivity of a new server-centric DCN, called BCDC, based on crossed cube with excellent performance. We prove that the $g$-restricted connectivity of BCDC is 4 for $n=3$ and $2n+g(n-2)-2$ for $n\geq 4$, where $0\leq g\leq n-3$, and the $h$-extra connectivity of BCDC is 4 for $n=3$ and $2n+h(n-2)-2$ for $n\geq 4$, where $0\leq h\leq n-3$.

Induced H-Packing k-Partition Problem in Certain Networks

A collection = {H1 ,H2 ,..., Hr } of induced sub graphs of a graph G is said to be sg-independent if (i) V(Hi ) V(Hj )= , i j, 1≤ i, j≤ r and (ii) no edge of G has its one end in Hi and the other end in Hj , i j, 1≤ i, j≤ r. If Hi H, ∀ i, 1≤ i ≤r, then is referred to as a H-independent set of G. Let be a perfect or almost perfect H-packing of a graph G. Finding a partition of such that is Hindependent set, ∀ i, 1 ≤ i ≤ k, with minimum k is called the induced H-packing kpartition problem of G. The induced H-packing k-partition number denoted by ipp(G,H) is defined as ipp(G,H) = min (G,H) where the minimum is taken over all H-packing of G. In this paper we obtain the induced H-packing k-partition number for Enhanced hypercube, Augmented Cubes and Crossed Cube networks where H is isomorphic to and .

Realizing Exchanged Crossed Cube Communication Patterns on Linear Array WDM Optical Networks

The exchanged crossed cube, denoted by [Formula: see text], is a novel interconnection network with fewer edges and smaller diameter compared to other variations of the corresponding hypercube. The linear array, denoted by [Formula: see text], is one of the most popular topologies in optical networks. This paper addresses the routing and wavelength assignment for realizing [Formula: see text] communication pattern on wavelength division multiplexing (WDM) optical network [Formula: see text], where [Formula: see text]. We prove that the congestion for [Formula: see text] on [Formula: see text] is equal to [Formula: see text], which is the lower bound of the minimum number of required wavelengths. In addition, an embedding scheme and an optimal wavelength assignment algorithm that achieve this bound are also proposed.