Embedded Edge-Connectivity Reliability Evaluation of Augmented Hypercube Interconnection Networks

Zhang, Mingzu; Liu, Hongxi; Li, Pingping

doi:10.1142/s0129054122500150

Cited by 2 publications

(2 citation statements)

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“…(n − t) for 1 ≤ t ≤ n − 1, where S n is the n-dimensional star graph. In Zhang et al [13], it is mainly proved that η t (AQ n ) = 2 t+1 (n − t) for 1 ≤ t ≤ n − 1, where S n is the n-dimensional augmented cube. The super embedded edge connectivity of S n and AQ n , and the super t-embedded edge connectivity of Q k n with t ≤ n − 2 and odd k ≥ 5 remain to be investigated.…”

Section: Discussionmentioning

confidence: 99%

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Minimum edge cuts of hypercubes and k-ary n-cubes leaving every fault-free node in given subnetworks

Yang,

Meng

2023

Preprint

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The hypercube and the $k$-ary $n$-cube are two leading interconnection networks for multiprocessor systems. {\it A $t$-embedded edge cut} of an $n$-dimensional recursive interconnection network $G_n$ is a set of edges whose removal separates $G_n$ and each vertex lies in a $t$-dimensional subnetwork of the residual network. The network $G_n$ is {\it super $t$-embedded edge connected} ({\it super-$\eta_t$} for short) if the deletion of an arbitrary minimum $t$-embedded edge cut of $G_n$ isolates a $t$-dimensional subnetwork $G_t$. In this note, we show that both the $n$-dimensional hypercube and the ternary $n$-cube are super-$\eta_t$ for $0\leq t\leq n-1$ except for the $2$D hypercube when $t=0$, and the $k$-ary $n$-cube with odd $k\geq 5$ is not super-$\eta_{n-1}$. An algorithm is proposed to obtain a minimum embedded-edge cut for hypercubes and $k$-ary $n$-cubes with odd $k\geq 3$.

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Section: Discussionmentioning

confidence: 99%

“…The t-embedded edge connectivity of several networks, such as the bubble-sort graph [6,9], the star graph [6,10], the n-dimensional hypercube Q n [6], the k-ary ncube Q k n [11,12] and the augmented hypercube [13] have been determined for some t. Particularly, Li et al [6] determined η t (Q n ) and Yang [12]…”

Section: Introductionmentioning

confidence: 99%