To find a cycle (resp. path) of a given length in a graph is the cycle (resp. path) embedding
problem. To find cycles of all lengths from its girth to its order in a graph is the pancyclic …

The-ary-cube is one of the most attractive interconnection networks for parallel and
distributed systems. Let be a set of faulty links in and let be a linear forest in such that. For …

Reliability evaluation of multiprocessor systems is of great significance to the design and
maintenance of these systems. As two generalizations of traditional edge connectivity, extra …

Abstract The 3-ary n-cube, denoted as Q n 3 Q _n^ 3, is an important interconnection
network topology proposed for parallel computers, owing to its many desirable properties …

The conditional diagnosability and the 2-extra connectivity are two important parameters to
measure ability of diagnosing faulty processors and fault-tolerance in a multiprocessor …

Reliability measure of multiprocessor systems is of significant importance to the design and
maintenance of multiprocessor systems. Based on edge connectivity, more refined …

The k-ary n-cube, Qnk, is one of the most popular interconnection networks. Let n≥ 2 and
k≥ 3. It is known that Qnk is a nonbipartite (resp. bipartite) graph when k is odd (resp. even) …

In this paper we give precise solutions to problems posed by Wang, An, Pan, Wang and Qu
and by Hsieh, Lin and Huang. In particular, we show that Q nk is bipanconnected and edge …

The k-ary n-cube is one of the most attractive interconnection networks for parallel and
distributed computing system. In this paper, we investigate hamiltonian cycle and path …

Graph embeddings play a significant role in the design and analysis of parallel algorithms. It
is a mapping of the topological structure of a guest graph G into a host graph H, which is …