Institute of Mathematics, Khawaja Fareed University of Engineering & Information Technology, Abu Dhabi Road, Rahim Yar Khan 64200, Pakistan.
Department of Mathematics and Statistics, College of Science, De La Salle University, 2401 Taft Avenue, Manila 1004, Philippines.
Molecules. 2023 Jan 3;28(1):452. doi: 10.3390/molecules28010452.
Entropy is a measure of a system's molecular disorder or unpredictability since work is produced by organized molecular motion. Shannon's entropy metric is applied to represent a random graph's variability. Entropy is a thermodynamic function in physics that, based on the variety of possible configurations for molecules to take, describes the randomness and disorder of molecules in a given system or process. Numerous issues in the fields of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines are resolved using distance-based entropy. These applications cover quantifying molecules' chemical and electrical structures, signal processing, structural investigations on crystals, and molecular ensembles. In this paper, we look at -Banhatti entropies using -Banhatti indices for C6H6 embedded in different chemical networks. Our goal is to investigate the valency-based molecular invariants and -Banhatti entropies for three chemical networks: the circumnaphthalene (CNBn), the honeycomb (HBn), and the pyrene (PYn). In order to reach conclusions, we apply the method of atom-bond partitioning based on valences, which is an application of spectral graph theory. We obtain the precise values of the first -Banhatti entropy, the second -Banhatti entropy, the first hyper -Banhatti entropy, and the second hyper -Banhatti entropy for the three chemical networks in the main results and conclusion.
熵是衡量系统分子无序或不可预测性的一种方法，因为功是由有序的分子运动产生的。香农熵度量被应用于表示随机图的可变性。熵是物理学中的热力学函数，它基于分子可以采取的各种可能构型，描述了给定系统或过程中分子的随机性和无序性。基于距离的熵在数学、生物学、化学图论、有机和无机化学等多个领域的众多问题得到了解决。这些应用包括量化分子的化学和电结构、信号处理、晶体结构研究和分子集合。在本文中，我们使用嵌入在不同化学网络中的 C6H6 的-Banhatti 指标来研究-Banhatti 熵。我们的目标是研究三种化学网络（circumnaphthalene（CNBn）、honeycomb（HBn）和 pyrene（PYn））的基于价的分子不变量和-Banhatti 熵。为了得出结论，我们应用了基于价的原子键划分方法，这是谱图理论的一种应用。在主要结果和结论中，我们获得了三种化学网络的第一-Banhatti 熵、第二-Banhatti 熵、第一超-Banhatti 熵和第二超-Banhatti 熵的精确值。
