论文标题
涉及超立方体网络的SM-λ属性的边缘耐受耐受性
Edge-fault-tolerance about the SM-λ property of hypercube-like networks
论文作者
论文摘要
网络的边缘耐受性对网络的设计和维护具有重要意义。对于任何连接的图形$ g $的顶点$ u $和$ v $，如果它们是由$ \ min \ {°_g（u）连接的，°_g（v）\} $ edge-dise偶口路径，那么$ g $ nat，则$ g $是强的menger enger enger gended connected（SM-$ pectect）。 有条件的边缘兑换率约为$ g $的sm-$λ$属性，书面$sm_λ^r（g）$，是$ m $的最大值，以至于$ g-f $仍然是任何边缘子集$ f $ a $ | f | f | f | f | f | f | f | f | \ leq m $和$Δ（g g-g-f $ geq r $）$ $ $ $ us $ us $ g f a $ g f a g f | 以前，$SM_λ^r（g）$的大多数确切值是针对$ r \ leq 2 $的一些知名网络，而在某些知名网络上的一些下限为$ r \ geq 3 $。在本文中，我们首先确定一般$ r $的$sm_λ^r（g）$的确切价值（简短的hl-networks（包括超橡胶，扭曲的立方体，交叉的立方体等），即一般$ r $，即$sm_λ^r（g_n）= 2^r（n-r（n-r）-n $ ge_n $ g_n $ ge_n $ ge_n $ nl $ g_n $， $ 1 \ leq r \ leq n-2 $。
The edge-fault-tolerance of networks is of great significance to the design and maintenance of networks. For any pair of vertices $u$ and $v$ of the connected graph $G$, if they are connected by $\min \{ °_G(u),°_G(v)\}$ edge-disjoint paths, then $G$ is strong Menger edge connected (SM-$λ$ for short). The conditional edge-fault-tolerance about the SM-$ λ$ property of $G$, written $sm_λ^r(G)$, is the maximum value of $m$ such that $G-F$ is still SM-$λ$ for any edge subset $F$ with $|F|\leq m$ and $δ(G-F)\geq r$, where $δ(G-F)$ is the minimum degree of $G-F$. Previously, most of the exact value for $sm_λ^r(G)$ is aimed at some well-known networks when $r\leq 2$, and a few of the lower bounds on some well-known networks for $r\geq 3$. In this paper, we firstly determine the exact value of $sm_λ^r(G)$ on class of hypercube-like networks (HL-networks for short, including hypercubes, twisted cubes, crossed cubes etc.) for a general $r$, that is, $sm_λ^r(G_n)=2^r(n-r)-n$ for every $G_n\in HL_n$, where $n\geq 3$ and $1\leq r \leq n-2$.
