锯齿形棱冠状体与星冕融合的度量维数和棱度量维数
Metric and Edge Metric Dimension of Zigzag Edge Coronoid Fused with Starphene
摘要：
设$Γ=(V,E)$是简单连通图。$d(α,ε)=min\{d(α, w), d(α, d\}$计算顶点$α\in V(Γ)$和边$ε=wd\in E(Γ)$之间的距离。如果$d(α, ε_{2})\neq d(α, ε_{1}\}$为$E(Γ)$，则称单个顶点$α$从$E(Γ)$识别（解析）两个不同的边$ε_{1}$和$ε_{2}$。如果来自$Γ$的每对不同边都被$U_{E}$的某个元素识别，则不同有序顶点的子集$U_{E}\subseteq V(Γ)$被称为$Γ$的边度量生成器。其中具有最小数目的元素的边缘度量生成器被称为$Γ$的边缘度量基。然后，$Γ$的该边缘度量基的基数被称为$Γ$的边缘度量维数，用$edim(Γ)$表示。使用图论术语研究化学结构的概念既吸引人又实用。它使化学研究人员能够更精确，更容易地检查各种化学拓扑结构和网络。在这篇文章中，我们调查了一个迷人的集群的有机化学作为一个结果的动机。我们考虑一个锯齿形边冠状面与星形面融合，并找到它的最小顶点和边度量生成元。
英文摘要：
Let $Γ=(V,E)$ be a simple connected graph. $d(α,ε)=min\{d(α, w), d(α, d\}$ computes the distance between a vertex $α\in V(Γ)$ and an edge $ε=wd\in E(Γ)$. A single vertex $α$ is said to recognize (resolve) two different edges $ε_{1}$ and $ε_{2}$ from $E(Γ)$ if $d(α, ε_{2})\neq d(α, ε_{1}\}$. A subset of distinct ordered vertices $U_{E}\subseteq V(Γ)$ is said to be an edge metric generator for $Γ$ if every pair of distinct edges from $Γ$ are recognized by some element of $U_{E}$. An edge metric generator with a minimum number of elements in it, is called an edge metric basis for $Γ$. Then, the cardinality of this edge metric basis of $Γ$, is called the edge metric dimension of $Γ$, denoted by $edim(Γ)$. The concept of studying chemical structures using graph theory terminologies is both appealing and practical. It enables chemical researchers to more precisely and easily examine various chemical topologies and networks. In this article, we investigate a fascinating cluster of organic chemistry as a result of this motivation. We consider a zigzag edge coronoid fused with starphene and find its minimum vertex and edge metric generators.
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。
