图的广义萨格勒布指数的锐界

arXiv - MATH - Combinatorics Pub Date : 2024-09-09 DOI:arxiv-2409.06081

Sanju Vaidya, Jeff Chang

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引用次数: 0

摘要

近四十年来，许多科学家利用图论建立了数学模型，用于分析各种化合物的结构和性质。在本文中，我们将建立基于顶点度的广义第一萨格勒布指数和共指数的公式和边界。此外，对于三角形和四角形自由图，我们将建立基于顶点 2 距离度的广义第一跃迁萨格勒布指数和 coindex 的公式和边界。此外，我们还将为各种类型的图建立广义第一萨格勒布指数和跃迁指数的锐界，并举例说明如何达到锐界。此外，我们还将找到回归模型，并比较第一萨格勒布指数和第一跃迁萨格勒布指数，以预测某些化合物（苯类烃）的某些理化性质。

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Sharp Bounds for Generalized Zagreb Indices of Graphs

In the last forty years, many scientists used graph theory to develop mathematical models for analyzing structures and properties of various chemical compounds. In this paper, we will establish formulas and bounds for generalized first Zagreb Index and coindex, which are based on degrees of vertices. In addition, for triangle and quadrangle free graphs, we will establish formulas and bounds for generalized first leap Zagreb Index and coindex, which are based on 2-distance degrees of vertices. Additionally, we will establish sharp bounds of generalized first Zagreb index and the leap index for various types of graphs and provide examples for which the sharp bounds are attained. In addition, we will find regression models and compare the first Zagreb index and the first leap Zagreb index for predicting some physicochemical properties of certain chemical compounds, benzenoid hydrocarbons.

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arXiv - MATH - Combinatorics

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