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, index, and index, for chain oxide network , chain silicate network , ortho chain , and para chain , for the first time. Moreover, analytically closed formulae for these structures are determined.

There are numeric numbers that define chemical descriptors that represent the entire structure of a graph, which contain a basic chemical structure. Of these, the main factors of topological indices are such that they are related to different physical chemical properties of primary chemical compounds. The biological activity of chemical compounds can be constructed by the help of topological indices. In theoretical chemistry, numerous chemical indices have been invented, such as the Zagreb index, the Randić index, the Wiener index, and many more. Hex-derived networks have an assortment of valuable applications in drug store, hardware, and systems administration. In this analysis, we compute the Forgotten index and Balaban index, and reclassified the Zagreb indices, $AB{C}_4$ index, and $G{A}_5$ index for the third type of hex-derived networks theoretically.

In chemical graph theory, a topological index is a numerical representation of a chemical network, while a topological descriptor correlates certain physicochemical characteristics of underlying chemical compounds besides its chemical representation. The graph plays a vital role in modeling and designing any chemical network. Simonraj et al. derived a new type of graphs, which is named a third type of hex-derived networks. In our work, we discuss the third type of hex-derived networks $HDN3(r)$ , $THDN3(r)$ , $RHDN3(r)$ , $CHDN3(r)$ , and compute exact results for topological indices which are based on degrees of end vertices.

Topological indices are numerical parameters of a molecular graph, which characterize its topology and are usually graph invariant. In quantitative structure-activity relationship/quantitative structure-property relationship study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC), and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we are taking Dominating David Derived networks, produced by honeycomb structure of dimension t and obtain analytical closed results of Multiplicative topological indices and acquire exact results of degree based indices.

In the research of QSAR and QSPR correlations, topological indices such as the Randi’c index, Zagreb index, ABC index, and geometric-arithmetic index have been proposed to analyze bio-compatibility of chemical compounds. Chemical graph theory is the combination of Chemistry and Graph theory, and this theory deals with the topology such as the mathematical study of isomerism and the development of topological indices which has applications in QSAR and QSPR. In this article, we consider the Octahedron networks and find out the above mentioned degree based topological indices.

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 GA entropy of HDN 1(n) and HDN 2(n).