Graphs are essential tools to illustrate relationships in given datasets visually. Therefore, generating graphs from another concept is very useful to understand it comprehensively. This paper will introduce a new yet simple method to obtain a graph from any finite affine plane. Some combinatorial properties of the graphs obtained from finite affine planes using this graph-generating algorithm will be examined. The relations between these combinatorial properties and the order of the affine plane will be investigated. Wiener and Zagreb indices, spectrums, and energies related to affine graphs are determined, and appropriate theorems will be given. Finally, a characterization theorem will be presented related to the degree sequences for the graphs obtained from affine planes.

中文翻译：

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仿射图及其拓扑指标

图形是必不可少的工具，可以直观地说明给定数据集中的关系。因此，从另一个概念生成图形对于全面理解它非常有用。本文将介绍一种新的但简单的方法来从任何有限的仿射平面获得图形。将检查使用此图生成算法从有限仿射平面获得的图的某些组合性质。将研究这些组合特性与仿射平面的顺序之间的关系。确定与仿射图有关的Wiener和Zagreb指数，频谱和能量，并给出适当的定理。最后，将给出与从仿射平面获得的图的度序列有关的表征定理。