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| ON THE CONDITIONAL EDGE CONNECTIVITY OF ENHANCED HYPERCUBE NETWORKS |
| Yanjuan Zhang,Hongmei Liu,Dan Jin |
| (College of Science China Three Gorges University, Yichang 443002, Hubei, PR China) |
| DOI： |
| Abstract: |
| Let $G = (V, E)$ be a connected graph and $m$ be a positive integer, the conditional edge connectivity $\lambda_{\delta}^{m}$ 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 $\lambda_{\delta}^{1}(Q_{n,k})=2n$, $\lambda_{\delta}^{2}(Q_{n,k})=4n-4$ $(2 \leq k \leq n - 1$, $n \geq 3)$ for $n$-dimensional enhanced hypercube $Q_{n,k}$. Meanwhile, another easy proof about $\lambda_{\delta}^{2}(Q_{n})=4n-8$, for $n \geq 3$ is proposed. The results of enhanced hypercube include the cases of folded hypercube. |
| Key words: interconnected networks; connectivity; conditional edge connectivity; fault tolerance; enhanced hypercube |