泡排序星图的边容错强Menger边连通度
Edge-fault-tolerant strong Menger edge connectivity of bubble-sort star graphs
摘要：
互连网络的连通度和边连通度决定了网络的容错性。互连网络通常被看作是一个连通图，其中顶点对应于处理器，边对应于两个不同处理器之间的链路。给定一个具有点集$V(G)$和边集$E(G)$的连通图$G$，如果对任意两个不同的点$u,v\in V(G)$，$u$和$v$之间存在$\min\{d_G(u),d_G(v)\}$边不交路，则$G$是强Menger边连通的.令$m$是具有$m\geq1$的整数。如果对于任何具有$|F_e|\leq m$的$F_e\subseteq E(G)$，$G-F_e$保持强Menger边连通，则$G$是$m$ -边容错强Menger边连通的。如果对于任何具有$|F_e|\leq m$和$δ(G-F_e)\geq2$的$F_e\subseteq E(G)$，$G-F_e$是强Menger边连通的，则$G$是$m$ -条件边容错强Menger边连通的。本文考虑$n$维泡排序星图$BS_n$。我们证明了$BS_n$是$(2n-5)$ -边容错强Menger边连通的$n\geq3$和$(6n-17)$ -条件边容错强Menger边连通的$n\geq4$ .此外，我们给出了一些例子来说明我们的结果是最优的。
英文摘要：
The connectivity and edge connectivity of interconnection network determine the fault tolerance of the network. An interconnection network is usually viewed as a connected graph, where vertex corresponds processor and edge corresponds link between two distinct processors. Given a connected graph $G$ with vertex set $V(G)$ and edge set $E(G)$, if for any two distinct vertices $u,v\in V(G)$, there exist $\min\{d_G(u),d_G(v)\}$ edge-disjoint paths between $u$ and $v$, then $G$ is strongly Menger edge connected. Let $m$ be an integer with $m\geq1$. If $G-F_e$ remains strongly Menger edge connected for any $F_e\subseteq E(G)$ with $|F_e|\leq m$, then $G$ is $m$-edge-fault-tolerant strongly Menger edge connected. If $G-F_e$ is strongly Menger edge connected for any $F_e\subseteq E(G)$ with $|F_e|\leq m$ and $δ(G-F_e)\geq2$, then $G$ is $m$-conditional edge-fault-tolerant strongly Menger edge connected. In this paper, we consider the $n$-dimensional bubble-sort star graph $BS_n$. We show that $BS_n$ is $(2n-5)$-edge-fault-tolerant strongly Menger edge connected for $n\geq3$ and $(6n-17)$-conditional edge-fault-tolerant strongly Menger edge connected for $n\geq4$. Moreover, we give some examples to show that our results are optimal.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
