Porphyrazine is a macrocyclic molecule that has potential uses in biology and materials research. In this work, we investigate the topological characteristics of porphyrazine via topological indices. These indices are important in QSPR and QSAR modeling because they aid in the analysis and prediction of physical, biological, and chemical properties associated with a specific chemical structure. In this paper, we investigate neighborhood M-polynomial and graph index-entropy of porphyrazine graph, deriving several topological indices based on neighborhood degree sum from it, and numerical computation and graphical interpretation are used to explain the results further. This research advances our understanding of the basic principles of physics and chemistry by shedding light on the intricate connections between biological processes, chemical reactivity, and molecular structure.

Topological indices are very important because they are used in the study of QSAR (Quantitative Structure-Activity Relationships) and QSPR (Quantitative Structure-Property Relationships) which are mathematical models that show the properties among physicochemical, environmental, and biological activity of a chemical structure. The chemical structure of a molecular graph is used to find the topological indices, which are widely used in theoretical chemistry, environmental chemistry, toxicology, and many others for correlation analysis. Topological indices are numerical values that helps us in measuring the physical and chemical properties of any molecule. In this article, we have calculated some degree-based topological indices of two categories of Metal-Organic Frameworks (MOFs), named as, CoBHT (cobalt butylated hydroxytoluene) and FeTPyP (Iron tetrakis pyridyl porphyrin)-CO (MOFs), also their graphical results are compared at the end.

Topological indices are numeric values of the chemical graph which describe the harmony of molecular structures and different properties of the chemical compound (like: melting point, boiling point, expansion, conduction or viscosity etc.). The Quantitative Structure Activity Relationship (QSAR) gives us prediction about biological activities of a chemical compound with the help of its chemical structure. The area of interest of this paper is to determine some of quantitative values (topological indices) of PolyPhenylene as it has remarkable characteristics like mechanical strength, compression strength, pressure resistance and many more, so that the QSAR analysis can be more reliable.

Porphyrazines (Pz) are porphyrinoids, which are macro-cyclic compounds made up of four in-dole rings. Pz has various potential and practical uses in health and technology due to their distinctive optical and electrochemical characteristics. Topological descriptors are numerical values given to molecular structures that may be used to predict specific physical characteristics. In this work, we have investigated topological features of the porphyrazine and tetrakis porphyrazine structure based on degree. We have calculated the closed forms of the Zagreb, Randic, geometric-arithmetic, harmonic, augmented and atom-bond connectivity (ABC) indices of the porphyrazine and tetrakis porphyrazine structures. The present research would be beneficial for understanding the structure's biological and chemical activity.

Topological co-indices are used to measure the strength of a relationship between molecular substance and its properties. A topological co-index is a mathematical representation of a molecular structure that integrates specific physical features of the basic molecular structure and its mathematical representation. Mathematical chemistry uses molecular graphs, which include edges that represent bonds between molecules and vertices that represent atoms, to integrate graph theory with science. Topological co-indices are a type of topological indices that considers separate vertices configurations that are numerical values of the atomic structures, which are used to describe and analyze the various chemical structures. Chemical graph theory brings up more possibilities for scientists. Topological co-indices are frequently used because through this we can save time by determining the topological indices instead of doing time-consuming tests in a research laboratory. In this article, we computed different topological co-indices for the chemical structure of Porphyrazine Network MCIPz(n).

Severe acute respiratory syndrome corona virus 2 (SARS-CoV-2) was identified in December (2019) as the cause of an outbreak of a respiratory sickness and has infected more than 190 million people all over the world. Numerous vaccines have been tested for corona virus (Covid-19) therapy such as Hydoxychloroquine, Ribavirin, sofosbuvir, tenofuvir and remdisivir. Hydroxychloroquine (HCQ), which is used in the treatment of malaria or treat infection, has recently been demonstrated for use in COVID-19 as an emergency therapy. The chemical substance HCQ is manufactured by rearranging the molecular structure of Ethylene oxide produced by human products, such as waxy maize starch. In medical science chemical properties, physical properties, pharmaceutical properties and biological properties of medicines are essential for designing of the drugs. These properties can be identified by topological indices. In this paper, we compute the temperature based topological indices of hydroxychoroquine HCQ-HES, and the discoveries will be beneficial in the development of novel drugs and vaccines in order to avoid and operation of corona virus (COVID-19).

A variety of graphical invariants have been described and tested, offering lots of applications in the fields of nanochemistry, computational networks and in different scientific research areas. One commonly studied group of invariants is the topological index, which allows to research the chemical, biological, and physical properties of a chemical structure. Topological indexes are numerical quantities that can be used to describe the properties of the molecular graph. In this article, we draw from the analytically closed formulas of certain molecular structures of coronavirus such as Ribavirin, Sofosbuvir and Oseltamivir by calculating temperature based topological indices.

Graph theory has many applications in chemistry while studying the molecular structure of chemicals, moreover number of its applications are also increasing day by day. Applying Quantitative Structure-Activity Relationship (QSAR) methods has become a challenging task due to lack of data and knowledge of chemical compounds. The computation of topological indices is a well known topic in chemical graph theory. These indices are used to investigate and evaluate the basic structures and groupings of molecule in chemical substances. In this paper, we have attempted to figure out some topological indices which are based on degree and reverse degree of Vanadium Carbide.

Organic compounds such as polyphenylene are very important and useful for the synthesis of many new organic compounds due to their physio-chemical properties. To ascertain these properties, one can use QSPR/QSAR methods which necessitate the computation of topological indices. The topological indices based on two newly introduced abstract notions of ev-degree and ve-degree are in practice to model numerous chemical properties as well as physical properties of organic, inorganic, hybrid, and biological compounds. In this study, we computed a certain number of topological indices for the chemical graph of polyphenylene network which will help to model some of its physio-chemical properties.

Organic material-based like silicon is important for the synthesis of new organic molecules, including the analysis of ultra-high protons catalyst and conductivity. More toward the molecular structural features of these compounds, the quantitative structure, properties and structural behavior of the silicon carbide compounds must be clarified. Topological indexes are an important method for understanding the fundamental topology of chemical structures for chemical compound investigation. In this paper, We have computed K Banhatti types indices and their variants for the structure silicon carbide Si2C3−I[r,s].

Nanomaterials are chemical compounds or substances which are moderately produced and used. Nanomaterials are engineered to reveal novel properties of nanocells that contrast with related non-visible substances, such as expanded consistency, conductivity or synthetic reaction. Topological indexes are quantities related to molecules that capture the harmony of molecular structures and give scientifically related properties, such as: viscosity, boiling point, radius of gravity, and so on. Their demands in genetics, chemistry, physics and nanoscience are infinite. The molecular topology of such compounds would be clarify by the quantitative structure properties relationship (QSPR) and quantitative structure activity relationship (QSAR). Two carbon nanosheet structures such as TC4C8(s) and dentritic nanostar have been discussed in this article, We have computed topological indices of these structures such as the first and the second K–Banhatti types indices and their variants.

Vanadium is naturally occurring fundamental element that has immense consumptions in industry and biological field. Vanadium (V) has different mineral and fossil fuel forms, most common are sandstones crude oil and coal. It is a d-transition metal, found in VA of the periodic table. Transition metal has characteristics to espouse multiple oxidation states +2,+3,+4,+5 of vanadium are useful. The ground-state electronic configuration of V is [ Ar] 3d3, 4s2 that contain 5 valance electrons. Vanadium element converts into ions, when lose valance electron so, it's has redox property. Chemical graph theory plays an important role in modeling and designing any chemical structure. The topological indices are the numerical invariants of a molecular graph and are very useful for predicting their physical properties. In this paper, we study the chemical graph of crystal structure ofVanadiumCarbide V2C. Also, we compute degree-based molecular descriptors (topological indices), namely first and second Zagreb index, first and second Zagreb coindices, Hyper-Zagreb index, first and second multiple Zagreb index and Redefined Zagreb index.

In this paper, we introduce the elimination ideal I-D(G) associated to a simple finite graph G. We obtain the upper bound of Castelnuovo-Mumford regularity of elimination ideal for various classes of graphs.

We give an uniform General Neron Desingularization for one dimensional local rings with respect to morphisms which coincide modulo a high power of the maximal ideal. The result has interesting applications in the case of Cohen-Macaulay rings.

We give algorithms to construct the Neron Desingularization and the easy case from [3] of the General Neron Desingularization.

In this paper we give an easy proof of the general Neron desingularization in the frame of regular morphism between Artinian local rings and Noetherian local rings of dimension one.