ChemicHull: 一种用于确定最大度数不超过3的极值化学图的在线工具
ChemicHull: an online tool for determining extremal chemical graphs of maximum degree at most 3 for any degree-based topological indices
AI总结：
ChemicHull是一种在线工具，用于确定任意度数基于拓扑指数的极值化学图，通过线性优化在多面体框架内分析化学图的极值特性。
摘要：
拓扑指数是图论描述符，其在数学化学中起着关键作用，捕捉分子的结构特征，并能预测其物理化学性质。一种广泛研究的拓扑指数类别，称为度数基于拓扑指数，是通过图中边的权重之和计算的，其中每条边的权重由仅取决于端点度数的公式确定。本研究专注于那些没有顶点度数超过3的化学图，这是共轭系统的模型。在多面体框架内，每个化学图被映射到三维空间中的一个点，从而通过在相应多面体上进行线性优化来确定任何度数基于拓扑指数的极值。在此框架内的分析揭示出极值仅限于少数化学图家族，这意味着某些化学图对任何度数基于拓扑指数都无法达到极值。本文的主要目的是介绍ChemicHull，我们开发的在线工具，用于确定和显示任意度数基于拓扑指数的极值化学图。为了展示该工具的力量，我们轻松地恢复了已建立的结果，强调了其在化学重要图类如化学树和单环化学图中的有效性。该工具还使识别了一个反驳先前发表的极值结果的反例。
英文摘要：
Topological indices are graph-theoretic descriptors that play a crucial role in mathematical chemistry, capturing the structural characteristics of molecules and enabling the prediction of their physicochemical properties. A widely studied category of topological indices, known as degree-based topological indices, are calculated as the sum of the weights of a graph's edges, where each edge weight is determined by a formula that depends solely on the degrees of its endpoints. This work focuses exclusively on chemical graphs in which no vertex has a degree greater than 3, a model for conjugated systems. Within a polyhedral framework, each chemical graph is mapped to a point in a three-dimensional space, enabling extremal values of any degree-based topological index to be determined through linear optimization over the corresponding polyhedron. Analysis within this framework reveals that extremality is limited to a small subset of chemical graph families, implying that certain chemical graphs can never attain extremality for any degree-based topological index. The main objective of this paper is to present ChemicHull, an online tool we have developed to determine and display extremal chemical graphs for arbitrary degree-based topological indices. To illustrate the power of this tool, we easily recover established results, emphasizing its effectiveness for chemically significant graph classes such as chemical trees and unicyclic chemical graphs. This tool also enabled the identification of a counterexample to a previously published extremal result concerning the Randić index.
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