Entropy is a thermodynamic function used in chemistry to determine the disorder and irregularities of molecules in a specific system or process. It does this by calculating the possible configurations for each molecule. It is applicable to numerous issues in biology, inorganic and organic chemistry, and other relevant fields. Metal–organic frameworks (MOFs) are a family of molecules that have piqued the curiosity of scientists in recent years. They are extensively researched due to their prospective applications and the increasing amount of information about them. Scientists are constantly discovering novel MOFs, which results in an increasing number of representations every year. Furthermore, new applications for MOFs continue to arise, illustrating the materials’ adaptability. This article investigates the characterisation of the metal–organic framework of iron(III) tetra-p-tolyl porphyrin (FeTPyP) and CoBHT (CO) lattice. By constructing these structures with degree-based indices such as the K-Banhatti, redefined Zagreb, and the atom-bond sum connectivity indices, we also employ the information function to compute entropies.

A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR)/quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Randić connectivity index, atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are used to predict the bioactivity of different chemical compounds. A dendrimer is an artificially manufactured or synthesized molecule built up from the branched units called monomers. In this paper, the fourth version of ABC index and the fifth version of GA index of certain families of nanostar dendrimers are investigated. We derive the analytical closed formulas for these families of nanostar dendrimers. The obtained results can be of use in molecular data mining, particularly in researching the uniqueness of tested (hyper-branched) molecular graphs.

Topological indices are invariant numerical quantities of a graph that give facts about the structure of graphs and are found to be very helpful in predicting the physical properties of aluminophosphates. The characteristics of aluminophosphates are similar to the characteristics of zeolites. Two examples of current applications are natural gas dehydration and humidity sensors. Researchers in chemistry and materials science are synthesizing new frameworks. There are many layers and holes in these substances. The technique used to predict natural behaviors among the physicochemical characteristics of chemical molecules in their basic network is known as topological indices. This study explains the vertex version of distance-based topological indices, the entropy of topological indices and their numerical analysis.

Chemical graph theory is a branch of mathematical chemistry which has an important outcome on the development of the chemical sciences. A chemical graph is a graph which is produced from some molecular structure by applying some graphical operations. The demonstration of chemical compounds and chemical networks with M-polynomials is a new idea and the M-polynomial of different molecular structures supports us to calculate many topological indices. A topological index is a numeric quantity that describes the whole structure of a molecular graph of the chemical compound and supports to understand its physical features, chemical reactivates and boiling activities. In this paper, we compute M-polynomial and topological indices of tadpole graph, then we recover numerous topological indices using the M-polynomial.

A topological index is a numerical measure that characterises the whole structure of a graph. Based on vertex degrees, the idea of an atom-bond connectivity index was introduced in chemical graph theory. Later, different versions of the ABC index were created, and some of these indices were recently designed. In this paper, we present the edge version of the atom-bond connectivity index, edge version of the multiplicative atom-bond connectivity index, and atom-bond connectivity temperature () index for the line graph of subdivision graph of tadpole graph , ladder graph , and wheel graph . Numerical simulation has also been shown for some novel families of atom-bond connectivity index comparing the three types of indices which can be useful for QSAR and QSPR studies.

Topological indices are numerical parameters associated with underlying topology of a molecular structure. They are correlated with several physio-chemical properties of chemical compounds. Recently, Euclidean metric based topological index has been introduced named as Sombor index. Therefore, in this article, we will discuss combinatorial aspects and compute Sombor index, average Sombor index and the reduced Sombor index of line graph of silicate carbides Si₂C₃-I[p, q].