Let $G$ be a hierarchical network (graph) with vertex set $V\left(G\right)$ and edge set $E\left(G\right)$. The preclusion set of the subnetwork $G^{\prime }$ (defined as a smaller network but with the same topological properties as the original one) in $G$ is a subset $V^{\prime }$ of $V\left(G\right)$ such that $G-V^{\prime }$ has no any subnetwork isomorphic to $G^{\prime }$. The preclusion number of $G^{\prime }$ in $G$ is $F\left(G^{\prime }\right)=min\{\left|V^{\prime }\right|:V^{\prime }\text{ is the preclusion set of }{G}^{\prime }\}$. Similarly, the edge preclusion set of $G^{\prime }$ in $G$ is a subset $E^{\prime }$ of $E\left(G\right)$ such that $G-E^{\prime }$ has no any subnetwork isomorphic to $G^{\prime }$. The edge preclusion number of $G^{\prime }$ in $G$ is $f\left(G^{\prime }\right)=min\{\left|E^{\prime }\right|:E^{\prime }\text{ is the edge preclusion set of }{G}^{\prime }\}$. The preclusion number and edge preclusion number are parameters which measure the fault tolerance of interconnection networks in the presence of failures. In this paper, we investigate the two parameters for a class of Cayley graphs $T_{2n+1}$ generated by the transposition tree similar to the star. Let $m$ be an integer with $0\le m\le n-1$, let $F(n,m)=F\left(T_{2(n-m)+1}\right)$, and let $f(n,m)=f\left(T_{2(n-m)+1}\right)$. We prove that $F(n,0)=f(n,0)=1$, $F(n,1)=2n(2n+1)$ with $2n+1$ prime, $f(n,1)\le 4n(2n+1)$ with $2n+1$ prime, $F(n,n-1)=\frac{(2n+1)!}{6}$, $f(n,n-1)=\frac{n(2n+1)!}{6}$, and $\left(\genfrac{}{}{0ex}{}{2n+1}{2m}\right)\left(2m\right)!\le F(n,m)\le f(n,m)\le \left(\genfrac{}{}{0ex}{}{n}{m}\right)\left(\genfrac{}{}{0ex}{}{2n+1}{2m}\right)\left(2m\right)!$. Finally, we prove that $F(n,m)$ is of order at most $n^{3m-1}$.

让 $G$ 是具有顶点集的分层网络（图形） $V（G）$ 和边缘集 $Ë（G）$。子网的排除集$G^{\prime }$ （定义为较小的网络，但具有与原始网络相同的拓扑属性） $G$ 是一个子集 $V^{\prime }$ 的 $V（G）$ 这样 $G-V^{\prime }$ 没有任何同构的子网 $G^{\prime }$。的排除数$G^{\prime }$ 在 $G$ 是 $F（G^{\prime }）=分\{\left|V^{\prime }\right|：V^{\prime }\text{ 是...的排除集 }{G}^{\prime }\}$。同样，边缘排除集$G^{\prime }$ 在 $G$ 是一个子集 ${Ë}^{\prime }$ 的 $Ë（G）$ 这样 $G-{Ë}^{\prime }$ 没有任何同构的子网 $G^{\prime }$。的边缘排除数$G^{\prime }$ 在 $G$ 是 $F（G^{\prime }）=分\{\left|{Ë}^{\prime }\right|：{Ë}^{\prime }\text{ 是的边缘排除集 }{G}^{\prime }\}$。排除编号和边缘排除编号是在出现故障时测量互连网络的容错能力的参数。在本文中，我们研究了一类Cayley图的两个参数${Ť}_{2ñ+\mathrm{1个}}$由转置树生成的类似于星星的。让$米$ 是一个整数 $0\le 米\le ñ-\mathrm{1个}$，让 $F（ñ，米）=F（{Ť}_{2（ñ-米）+\mathrm{1个}}）$， 然后让 $F（ñ，米）=F（{Ť}_{2（ñ-米）+\mathrm{1个}}）$。我们证明$F（ñ，0）=F（ñ，0）=\mathrm{1个}$， $F（ñ，\mathrm{1个}）=2ñ（2ñ+\mathrm{1个}）$ 与 $2ñ+\mathrm{1个}$ 主要， $F（ñ，\mathrm{1个}）\le 4ñ（2ñ+\mathrm{1个}）$ 与 $2ñ+\mathrm{1个}$ 主要， $F（ñ，ñ-\mathrm{1个}）=\frac{（2ñ+\mathrm{1个}）！}{6}$， $F（ñ，ñ-\mathrm{1个}）=\frac{ñ（2ñ+\mathrm{1个}）！}{6}$和 $\left(\genfrac{}{}{0ex}{}{2ñ+\mathrm{1个}}{2米}\right)（2米）！\le F（ñ，米）\le F（ñ，米）\le \left(\genfrac{}{}{0ex}{}{ñ}{米}\right)\left(\genfrac{}{}{0ex}{}{2ñ+\mathrm{1个}}{2米}\right)（2米）！$。最后，我们证明$F（ñ，米）$ 最多是有秩序的 ${ñ}^{3米-\mathrm{1个}}$。