Abstract A topological index is actually designed by transforming a chemical structure into a number. Topological index is a graph invariant which characterizes the topology of the graph and remains invariant under graph automorphism. Eccentricity based topological indices are of great importance and play a vital role in chemical graph theory. In this article, we consider a graph (non-zero component graph) associated to a finite dimensional vector space over a finite filed in the context of the following eleven eccentricity based topological indices: total eccentricity index; average eccentricity index; eccentric connectivity index; eccentric distance sum index; adjacent distance sum index; connective eccentricity index; geometric arithmetic index; atom bond connectivity index; and three versions of Zagreb indices. Relationship of the investigated indices and their dependency with respect to the involved parameters are also visualized by evaluating them numerically and by plotting their results.

中文翻译：

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与有限维向量空间相关联的图的偏心拓扑特性

摘要 拓扑索引实际上是通过将化学结构转化为数字来设计的。拓扑索引是一种图不变量，它表征了图的拓扑结构，并在图自同构下保持不变。基于偏心率的拓扑指数非常重要，在化学图论中起着至关重要的作用。在本文中，我们在以下 11 个基于偏心的拓扑指数的上下文中考虑与有限域上的有限维向量空间相关联的图（非零分量图）：总偏心指数；平均偏心指数；偏心连通指数；偏心距离总和指数；相邻距离总和指数；连接偏心率指数；几何算术指数；原子键连接指数；和三个版本的萨格勒布指数。