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 ℓ-component connectivity (or ℓ-connectivity for short) of a graph G, denoted by κ ℓ (G), is
the minimum number of vertices whose removal from G results in a disconnected graph with …

As an enhancement on the hypercube Qn, the augmented cube AQn, proposed by
Choudum and Sunitha [SA Choudum, V. Sunitha, Augmented cubes, Networks, 40 …

In this paper, we investigate the fault-tolerant capabilities of the k-ary n-cubes for even
integer k with respect to the hamiltonian and hamiltonian-connected properties. The k-ary n …

The protection routing uses the multi-paths technique for integrating route discovery and
route maintenance mechanisms in a network, and thus it can tolerate the failure of one …

A graph G=(V, E) is said to be pancyclic if it contains fault-free cycles of all lengths from 4 to|
V| in G. Let F/sub v/and F/sub e/be the sets of faulty nodes and faulty edges of an n …

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 …

Independent spanning trees (ISTs) on networks have applications in networks such as
reliable communication protocols, the multi-node broadcasting, one-to-all broadcasting …

A bipartite graph G is bipancyclic if G has a cycle of length l for every even 4⩽ l⩽| V (G)|. For
a bipancyclic graph G and any edge e, G is edge-bipancyclic if e lies on a cycle of any even …

A graph G is said to be conditional k-edge-fault pancyclic if after removing k faulty edges
from G, under the assumption that each node is incident to at least two fault-free edges, the …