论文标题
存在最佳连接节点可靠性的最佳远程图形
Existence of Optimally-Greatest Digraphs for Strongly Connected Node Reliability
论文作者
论文摘要
在本文中，我们介绍了一种新模型，以研究网络可靠性，并使用节点失败。该模型是强烈连接的节点可靠性，是节点可靠性的定向变体，并衡量操作顶点诱导强烈连接的子数据的概率。如果我们仅限于具有$ n $顶点的定向图，而$ n+1 \ leq m \ leq 2n-3 $或$ m = 2n $ arcs，则不存在最佳最佳的挖掘。此外，当顶点在零接近零一接近的概率$ p $上运行时，我们研究了最优质的定向循环图。 特别是，我们表明图$γ\ left（\ mathbb {z} _n，\ {1，-1 \} \ right）$对于$ p $接近零的$ p $的最佳优势。然后，我们确定图形$γ\ left（\ mathbb {z} _ {n}，\ {1，\ frac {n+2} {2} {2} \} \ right）$在$ n $时，$ p $的值是最佳的。接下来，我们表明图$γ\ left（\ mathbb {z} _ {n}，\ {1,2（3^{ - 1}）\} \ right）$在$ n $中奇怪且不划分的$ n $时，$ p $的最佳值最佳，而不是三个$ n $ $γ\ left（\ mathbb {z} _ {n}，\ {1,3（2^{ - 1}）\} \ right）$是最佳的$ p $值，当$ n $ of n $ off of $ n $是奇数和三个。我们以关于开放问题的讨论结束。
In this paper, we introduce a new model to study network reliability with node failures. This model, strongly connected node reliability, is the directed variant of node reliability and measures the probability that the operational vertices induce a subdigraph that is strongly connected. If we are restricted to directed graphs with $n$ vertices and $n+1\leq m\leq 2n-3$ or $m=2n$ arcs, an optimally-greatest digraph does not exist. Furthermore, we study optimally-greatest directed circulant graphs when the vertices operate with probability $p$ near zero and near one. In particular, we show that the graph $Γ\left(\mathbb{Z}_n,\{1,-1\}\right)$ is optimally-greatest for values of $p$ near zero. Then, we determine that the graph $Γ\left(\mathbb{Z}_{n},\{1,\frac{n+2}{2}\}\right)$ is optimally-greatest for values of $p$ near one when $n$ is even. Next, we show that the graph $Γ\left(\mathbb{Z}_{n},\{1,2(3^{-1})\}\right)$ is optimally-greatest for values of $p$ near one when $n$ is odd and not divisible by three and that $Γ\left(\mathbb{Z}_{n},\{1,3(2^{-1})\}\right)$ is optimally-greatest for values of $p$ near one when $n$ is odd and divisible by three. We conclude with a discussion of open problems.
