A topological index of graph G is a numerical quantity which describes its topology. If it is applied to molecular structure of a chemical compounds then it reflects the theoretical properties of the chemical compounds. In this article, well-known degree based topological indices are applied on chemical structures of medicine used for treatment of breast cancer. Chemical structure is considered as graph, where elements are taken as vertices and bounds between them are taken as edges. Further, QSPR analysis of said topological indices are discussed and it is shown that these topological indices are highly correlated with the physical properties of chemical compounds used for the treatment of breast cancer.

Corona virus cause diseases ranging from the common cold to Severe Acute Respiratory Syndrome (SARS). Several therapeutic agents have been evaluated for the treatment of Covid-19, but none have yet been shown to be efficacious. Remdesivir Gilead Sciences number (GS-5734), an inhibitor of the viral RNA-dependent, RNA polymerase with inhibitory activity against SARS-CoV and the Middle East respiratory syndrome (MERS-CoV), was identified early as a promising therapeutic candidate for Covid-19 because of its ability to inhibit SARS-CoV-2 invitro. Knowledge about the potential efficacy of Remdesivir against corona viruses has been restricted to in vitro studies and animal models. However, information related to COVID-19 is rapidly growing. Several clinical trials are ongoing for the management of COVID-19 using Remdesivir. Efficacy of Remdesivir (GS-5734) against Ebola virus has been demonstrated. In the field of Medical Science, concerning the definition of the topological index on the molecular structure and corresponding medical, biological, chemical, pharmaceutical properties of drugs can be studied by the topological index calculation. In this paper, we compute some reverse topological indices namely, the reverse general Randic index, the reverse atom bond connectivity index, the reverse geometric arithmetic index, the reverse forgotten index, the reverse Balaban index and the reverse Zagreb type indices.

Entropy is a thermodynamic function in chemistry that reflects the randomness and disorder of molecules in a particular system or process based on the number of alternative configurations accessible to them. Distance-based entropy is used to solve a variety of difficulties in biology, chemical graph theory, organic and inorganic chemistry, and other fields. In this article, the characterization of the crystal structure of niobium oxide and a metal–organic framework is investigated. We also use the information function to compute entropies by building these structures with degree-based indices including the K-Banhatti indices, the first redefined Zagreb index, the second redefined Zagreb index, the third redefined Zagreb index, and the atom-bond sum connectivity index.

The threat of developing a cancer therapy has been there for the past two to three decades. Almost 10 million people worldwide are affected by this illness each year. Anticancer medications are those that are used to treat cancer, a malignant condition. These anticancer medications come in a variety of types, such as hormones, antimetabolites, and alkalizing agents. Numerous studies demonstrate a close relationship between the chemical structure of anticancer drugs and alkane characteristics including boiling, melting, and enthalpy. Some antiviral medications that are thought to hold promise for the treatment of cancer are examined in the planned research. For the chemical graphs of these medications, ST-polynomials based on status distance are computed. Numerous topological indices (TI) that depend on the status distance may be constructed by applying these polynomials. Additionally, the TIs are used in the creation of the QSPR models to estimate some of the physicochemical characteristics of these medications. Curve fitting is used to produce the QSPR research.

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.

In this article we discuss the reverse degree based topological indices for planar metal-organic networks like transition metal (TM) of the three-dimensional series such as: Ti, V, Cr, $\dots ,$ or Zn, phthalocyanine, and tetracyanobenzene (TCNB) as free-standing sheets. In distinction, the TM-TCNB networks are metallic at least in one revolutionary orientation and demonstrate long-range ferromagnetic connect in case for magnetic erection, which illustrate ideal entrant and a stimulating prospect of unequaled applications in spintronics. Topological indices are numerical variables of a graph which describe its topology and are usually graph invariant. We have computed the reverse degree based topological indices like the reverse general Randic index, the reverse Balaban index, the reverse atom bond connectivity index, the reverse geometric index, the reverse Zagreb type indices, and the reverse augmented Zagreb index for this metal-organic networks TM-TCNB.