A novel geometric method is proposed for constructing vertex-degree-based molecular structure descriptors (topological indices). The model is based on an ellipse whose focal points represent the degrees of a pair of adjacent vertices. This approach enables a geometric interpretation of several previously known topological indices, and lead to design of a few new. The area of the ellipse induces a vertex-degree-based topological index of remarkable simplicity, which we call elliptic Sombor index(). The main mathematical properties of are established, especially its relations to other, earlier known, indices. Then the applicative potential of is analyzed.

中文翻译：

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基于顶点度的拓扑指数的几何方法——椭圆Sombor指数、理论与应用

提出了一种新的几何方法来构造基于顶点度的分子结构描述符（拓扑索引）。该模型基于椭圆，其焦点表示一对相邻顶点的度数。这种方法能够对几个先前已知的拓扑指数进行几何解释，并导致一些新的拓扑指数的设计。椭圆的面积产生了一个非常简单的基于顶点度的拓扑指数，我们称之为椭圆 Sombor 指数（）。主要数学性质已建立，特别是其与其他早期已知指数的关系。那么应用潜力被分析。