Topology is the mathematical study of the geometric and spatial properties that remain unchanged under continuous transformations of a graph's shape and size. In chemical graph theory, topological indices are used to quantify various chemical properties of molecules. These indices are derived from the topological structure of a graph and are crucial in understanding the valency of a chemical substance, which is determined by the number of surrounding atoms in its molecular structure. Topological indices are connected to numerous physicochemical properties, such as vapor pressure, stability, and elastic energy. In molecular structures, topological indices provide a numerical representation of the connections between molecules. In theoretical chemistry, these indices are widely used to simulate the physicochemical characteristics of complex compounds. QSAR/QSPR studies rely heavily on topological indices to predict physical and chemical properties. This article explores the hex-derived network and its first two types, calculating reversed degree-based topological indices for these networks.

Hex-derived network has an assortment of significant applications in medicine store, equipment, and network organization. Graph entropy depends upon distribution probability of vertex set and on graph itself. There are numerous issues in discrete math, software engineering, statistics, and data innovation where graph entropies are utilized to portray the reasonable constructions. In this paper, we talk about hex-derived network of type 3 denoted as HDN 3 n . We likewise figure degree-based entropies, for example, Randic’, ABC, and GA entropy of HDN 3 n .

Chemical graph theory is the combination of mathematical graph theory and chemistry. To analyze the biocompatibility of the compounds, topological indices are used in the research of QSAR/QSPR studies. The degree-based entropy is inspired by Shannon’s entropy. The connectivity pattern such as planar octahedron network is used to predict physiochemical activity. In this article, we present some degree-based entropies of planar octahedron network.

A graph’s entropy is a functional one, based on both the graph itself and the distribution of probability on its vertex set. In the theory of information, graph entropy has its origins. Hex-derived networks have a variety of important applications in medication store, hardware, and system administration. In this article, we discuss hex-derived network of type 1 and 2, written as HDN 1 n and HDN 2 n , respectively of order n . We also compute some degree-based entropies such as Randić, ABC , and G A entropy of HDN 1 n and HDN 2 n .

Structure-based topological descriptors of chemical networks enable us the prediction of physico-chemical properties and the bioactivities of compounds through QSAR/QSPR methods. Topological indices are the numerical values to represent a graph which characterises the graph. One of the latest distance-based topological index is the Mostar index. In this paper, we study the Mostar index, Szeged index, PI index, ABCGG index, and NGG index, for chain oxide network COXn , chain silicate network CSn , ortho chain Sn , and para chain Qn , for the first time. Moreover, analytically closed formulae for these structures are determined.

A graph’s entropy is a functional one, based on both the graph itself and the distribution of probability on its vertex set. In the theory of information, graph entropy has its origins. Dominating David derived networks have a variety of important applications in medication store, hardware, and system administration. In this study, we discuss dominating David derived network of type 1, 2, and 3 written as D1n, D2n, and D3n, respectively of order n. We also compute some degree-based entropies such as Randić, ABC, and GA entropy of D1n, D2n, and D3n.