双反棱柱及其相关图的容错可解性
On Fault-Tolerant Resolvability of Double Antiprism and its related Graphs
摘要：
对于一个连通图$Γ=(V,E)$，如果到$V$中顶点的距离向量对于每个$u^{i}\in V(Γ)$是唯一的，则称$Γ=(V,E)$中有序顶点的子集$R$是$Γ$中的一个分解集. $Γ$的度量维数是这样的集合$R$的最小基数。如果$R\setminus \{u^{i}\}$仍然是一个解析集$\forall$ $u^{i}\in R$，则$R$称为$Γ$的容错解析集（FTRS），其最小基数是$Γ$的容错度量维数（FTMD）.在这篇文章中，我们引入了一个独立的容错解决集（IFTRS）的概念，并研究它的几个著名的图。我们还表明，FTMD是四个密切相关的家庭凸多面体在文献中（即，双反棱镜$\mathbb{A}_{n}$、$S_{n}$和$T_{n}$）。
英文摘要：
For a connected graph $Γ=(V,E)$, a subset $R$ of ordered vertices in $V$ is said to be a resolving set in $Γ$, if the vector of distances to the vertices in $R$ is unique for each $u^{i}\in V(Γ)$. The metric dimension of $Γ$ is the minimum cardinality of such a set $R$. If $R\setminus \{u^{i}\}$ is still a resolving set $\forall$ $u^{i}\in R$, then $R$ is called a fault-tolerant resolving set (FTRS) for $Γ$ and its least cardinality is the fault-tolerant metric dimension (FTMD) of $Γ$. In this article, we introduce the concept of an independent fault-tolerant resolving set (IFTRS) and investigate it for several well-known graphs. We also show that the FTMD is four for three closely related families of convex polytopes available in the literature (viz., double antiprism $\mathbb{A}_{n}$, $S_{n}$, and $T_{n}$).
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。
