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 locally twisted cube is a variation of hypercube, which possesses some properties
superior to the hypercube. In this paper, we investigate the edge-fault-tolerant hamiltonicity …

This paper considers the problem of many-to-many disjoint paths in the hypercube Qn with
fv faulty vertices and fe faulty edges, and obtains the following result. For any integer k with …

A bipartite graph G=(V, E) is said to be bipancyclic if it contains a cycle of every even length
from 4 to| V|. Furthermore, a bipancyclic G is said to be edge-bipancyclic if every edge of G …

The augmented cube is a variation of hypercubes, it possesses many superior properties. In
this paper, we show that, for any n-dimensional augmented cube (n⩾ 3) with faulty edges up …

The connectivity is an important criteria to measure the fault-tolerant performance of a graph.
However, the connectivity based on the condition of the set of arbitrary faulty nodes is …

A graph is said to be pancyclic if it contains cycles of every length from its girth to its order
inclusive; and a bipartite graph is said to be bipancyclic if it contains cycles of every even …

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 …

In this paper, we study fault-tolerant routing in bijective connection networks with restricted
faulty edges. First, we prove that the probability that all the incident edges of an arbitrary …

Let FFv (respectively, FFe) be the set of faulty vertices (respectively, faulty edges) in an n-
dimensional folded hypercube FQn. In this paper, we show that FQn− FFv− FFe contains a …