A topological index, which is a number, is connected to a graph. It is often used in chemometrics, biomedicine, and bioinformatics to anticipate various physicochemical properties and biological activities of compounds. The purpose of this article is to encourage original research focused on topological graph indices for the drugs azacitidine, decitabine, and guadecitabine as well as an investigation of the genesis of symmetry in actual networks. Symmetry is a universal phenomenon that applies nature’s conservation rules to complicated systems. Although symmetry is a ubiquitous structural characteristic of complex networks, it has only been seldom examined in real-world networks. The $\overline{M}$-polynomial, one of these polynomials, is used to create a number of degree-based topological coindices. Patients with higher-risk myelodysplastic syndromes, chronic myelomonocytic leukemia, and acute myeloid leukemia who are not candidates for intense regimens, such as induction chemotherapy, are treated with these hypomethylating drugs. Examples of these drugs are decitabine (5-aza-20-deoxycytidine), guadecitabine, and azacitidine. The $\overline{M}$-polynomial is used in this study to construct a variety of coindices for the three brief medicines that are suggested. New cancer therapies could be developed using indice knowledge, specifically the first Zagreb index, second Zagreb index, F-index, reformulated Zagreb index, modified Zagreb, symmetric division index, inverse sum index, harmonic index, and augmented Zagreb index for the drugs azacitidine, decitabine, and guadecitabine.

A topological index is a number that is connected to a chemical composition in order to correlate a substance’s chemical makeup with different physical characteristics, chemical reactivity, or biological activity. It is common to model drugs and other chemical substances as different forms, trees, and graphs. Certain physico-chemical features of chemical substances correlate better with degree-based topological invariants. Predictions concerning the dynamics of the continuing pandemic may be made with the use of the graphic theoretical approaches given here. In Networks, the degree entropy of the epidemic and related trees was computed. It highlights the essay’s originality while also implying that this piece has improved upon prior literature-based realizations. In this paper, we study an important degree-based invariant known as the inverse sum indeg invariant for a variety of graphs of biological interest networks, including the corona product of some interesting classes of graphs and the pandemic tree network, curtain tree network, and Cayley tree network. We also examine the inverse sum indeg invariant features for the molecular graphs that represent the molecules in the bicyclic chemical graphs.

The severe acute metabolic process syndrome coronavirus-2 (SARS-CoV-2) virus strain causes an unique Corona viral (COVID-19) disease. It was initially documented in the foreign country of China, and it has since spread around the world. Fever, cough, and runny nose are among the symptoms of this illness, which mostly affects the respiratory system. The peculiar thing is that there is no therapy or vaccine available for this sickness. Clinical trials for a corona virus vaccine are still ongoing, with the vaccine likely to be available by 2021. Until then, the only way to deal with or control the virus’s spread is to take preventative precautions. The numerical descriptors of a molecule structure obtained by the molecular graph are known as topological indices. These can be utilized in structure-property relationship (QSPR) and structure-activity relationship (QSAR) investigations to learn a lot about a molecule’s physicochemical and biological properties. Lopinavir, ritonavir, arbidol, thalidomide, chloroquine, hydroxy-chloroquine, theaflavin, and remdesivir are investigated in this research as crucial lights in COVID-19 treatment. For chemical graphs of these medications, some status distance-based topological indices are constructed. Furthermore, these topological indices are used in the QSPR models to estimate some of the medications’ physicochemical properties. The results of the QSPR experiments, which were acquired using the polynomial regression technique, can contribute in the development of new drugs for the treatment of COVID-19.

In Sri Lanka as well as the rest of the globe, cancer is the top cause of mortality. One of the key medicines in treating tumors is anticancer medications and delivery dendrimers. To prevent the formation of the rapid proliferation of cancer cells, several tests were carried out. Because of this, research on dendrimers and anti-cancer medications is crucial. Topological indices (TIs) are molecular descriptors numerical values corresponding to the physical characteristics of a molecule’s chemical structure. It costs money to determine a molecule’s physical characteristics in a lab since it takes a lot of materials, medications, and time. Therefore, the relevant information about molecules may be obtained by computing TIs. This study’s goals are to compute hitherto uncalculated eccentricity-based TIs for various anticancer structures and to use curvilinear regression models to forecast the physical characteristics of particular anticancer medications. These anticancer medications were given different TIs developed in this work, allowing the researchers to understand the physical, physicochemical, and chemical characteristics related to them. In addition comparative study of the novel indices with some well-known and mostly used indices in structure–property modeling and anticancer drugs in performed.

The reformulated Zagreb index (or) RZ-invariant of a connected graph G is defined as RZ(G) = Sigma(a1a2 is an element of Sigma(G))(d(G)(a(1))+d(G)(a(2))-2)(2), where d(g)(a(1)) is the degree of a vertex a(1) in G. In this paper, we study the RZ-invariants for vertex version of F-join of given general graphs which are related to subdivision and total graph.