论文标题
一种新颖的视图：边缘等级方法和几种互连网络条件边缘连接性的可靠性评估
A novel view: edge isoperimetric methods and reliability evaluation of several kinds of conditional edge-connectivity of interconnection networks
论文作者
论文摘要
某些平行系统和分布式系统的互连网络的可靠性评估和容错性在各种链接故障的假设下分别讨论，以不同的$ \ Mathcal {p} $ - 条件边缘连接性。借助Edge Isoperimetric问题在组合学方面的方法，本文主要提供一种新颖而统一的观点，以调查$ \ Mathcal {p} $ - 有条件的锤子图$ k_ {l}^{n} $，以满足每个最小值$ \ nimim $ \ natime griendity grite Edge的属性， $ k_ {l}^{n} $仅分为两个组件，例如$ l^{t} $ - 额外的边缘连接性，$ t $ - embedded edge-ednectivity，循环边缘连接性，$（l-1）t $（l-1）t $ -super-super endecontivity，$（l-1）等级边缘连接性。它们以$（l-1）（n-t）l^{t} $的形式共享相同的值（循环边缘连接性除外），这相当于最小数量的链接故障数量，导致$ l $ -ary-y-ar-n $ n $ diebemential-demensional-demensional sublayer来自$ k_ {l}^n} $。此外，我们还获得了$ h $ -extra edge-connectitive的确切值和$ h $ - th hamming图的等值范围的边缘连接性$ k_ {l}^{n} $ for $ h \ h \ leq l^leq l^{\ lfloor {\ lfloor {\ lfloor {\ frac {\ frac {n} {对于情况，$ l = 2 $，$ k_2^n = q_n $是$ n $ dimensional hypercube。我们的结果可以应用于更具通用类别的网络类别，称为$ n $ dim份的族裔连接网络，该网络包含高管，扭曲的立方体，交叉的立方体，莫比乌斯立方体，本地扭曲的立方体等。我们的结果改善了有关此主题的几个先前结果。
Reliability evaluation and fault tolerance of an interconnection network of some parallel and distributed systems are discussed separately under various link-faulty hypotheses in terms of different $\mathcal{P}$-conditional edge-connectivity. With the help of edge isoperimetric problem's method in combinatorics, this paper mainly offers a novel and unified view to investigate the $\mathcal{P}$-conditional edge-connectivities of hamming graph $K_{L}^{n}$ with satisfying the property that each minimum $\mathcal{P}$-conditional edge-cut separates the $K_{L}^{n}$ just into two components, such as $L^{t}$-extra edge-connectivity, $t$-embedded edge-connectivity, cyclic edge-connectivity, $(L-1)t$-super edge-connectivity, $(L-1)t$-average edge-connectivity and $L^{t}$-th isoperimetric edge-connectivity. They share the same values in form of $(L-1)(n-t)L^{t}$ (except for cyclic edge-connectivity), which equals to the minimum number of links-faulty resulting in an $L$-ary-$n$-dimensional sub-layer from $K_{L}^{n}$. Besides, we also obtain the exact values of $h$-extra edge-connectivity and $h$-th isoperimetric edge-connectivity of hamming graph $K_{L}^{n}$ for each $h\leq L^{\lfloor {\frac{n}{2}} \rfloor}$. For the case $L=2$, $K_2^n=Q_n$ is $n$-dimensional hypercube. Our results can be applied to more generalized class of networks, called $n$-dim-ensional bijective connection networks, which contains hypercubes, twisted cubes, crossed cubes, Möbius cubes, locally twisted cubes and so on. Our results improve several previous results on this topic.
