@Article{AAM-34-3,
author = {Zhang, Yanjuan and Liu, Hongmei and Jin, Dan},
title = {On the Conditional Edge Connectivity of Enhanced Hypercube Networks},
journal = {Annals of Applied Mathematics},
year = {2018},
volume = {34},
number = {3},
pages = {319--330},
abstract = {<p style="text-align: justify;">Let $G = (V, E)$ be a connected graph and $m$ be a positive integer, the
conditional edge connectivity $\lambda^m_\delta$ is the minimum cardinality of a set of edges,
if it exists, whose deletion disconnects $G$ and leaves each remaining component
with minimum degree $\delta$ no less than $m.$ This study shows that $\lambda^1_\delta (Q_{n,k}) = 2n,$ $λ^2_\delta(Q_{n,k}) = 4n − 4$$(2 ≤ k ≤ n − 1, n ≥ 3)$ for $n$-dimensional enhanced
hypercube $Q_{n,k}.$ Meanwhile, another easy proof about $\lambda^2_\delta (Q_n) = 4n − 8,$ for $n ≥ 3$ is proposed. The results of enhanced hypercube include the cases of
folded hypercube.</p>},
issn = {},
doi = {https://doi.org/2018-AAM-20580},
url = {https://global-sci.com/article/72724/on-the-conditional-edge-connectivity-of-enhanced-hypercube-networks}
}