English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The edge-fault-tolerance of networks is of great significance to the designand maintenance of networks. For any pair of vertices $u$ and $v$ of theconnected graph $G$, if they are connected by $\min \{ \deg_G(u),\deg_G(v)\}$edge-disjoint paths, then $G$ is strong Menger edge connected (SM-$\lambda$ forshort).  The conditional edge-fault-tolerance about the SM-$ \lambda$ property of $G$,written $sm_\lambda^r(G)$, is the maximum value of $m$ such that $G-F$ is stillSM-$\lambda$ for any edge subset $F$ with $|F|\leq m$ and $\delta(G-F)\geq r$,where $\delta(G-F)$ is the minimum degree of $G-F$.  Previously, most of the exact value for $sm_\lambda^r(G)$ is aimed at somewell-known networks when $r\leq 2$, and a few of the lower bounds on somewell-known networks for $r\geq 3$. In this paper, we firstly determine theexact value of $sm_\lambda^r(G)$ on class of hypercube-like networks(HL-networks for short, including hypercubes, twisted cubes, crossed cubesetc.) for a general $r$, that is, $sm_\lambda^r(G_n)=2^r(n-r)-n$ for every$G_n\in HL_n$, where $n\geq 3$ and $1\leq r \leq n-2$.

Edge-fault-tolerance about the SM-{\lambda} property of hypercube-like networks