In order to identify the basic structural properties of a network such as connectedness, centrality, modularity, accessibility, clustering, vulnerability, and robustness, we need distance-based parameters. A number of tools like these help computer and chemical scientists to resolve the issues of informational and chemical structures. In this way, the related branches of aforementioned sciences are also benefited with these tools as well. In this paper, we are going to study a symmetric class of networks called convex polytopes for the upper and lower bounds of fractional metric dimension (FMD), where FMD is a latest developed mathematical technique depending on the graph-theoretic parameter of distance. Apart from that, we also have improved the lower bound of FMD from unity for all the arbitrary connected networks in its general form.

中文翻译：

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关于凸多面体的分数维数

为了识别网络的基本结构特性，例如连通性、中心性、模块化、可访问性、聚类、脆弱性和稳健性，我们需要基于距离的参数。许多类似的工具帮助计算机和化学科学家解决信息和化学结构的问题。通过这种方式，上述科学的相关分支也受益于这些工具。在本文中，我们将研究一类对称网络，称为分数度量维数 (FMD) 的上限和下限的凸多面体，其中 FMD 是一种最新开发的数学技术，取决于距离的图论参数。除此之外，我们还改进了所有任意连接网络的统一形式的 FMD 下界。