A nanostructure belong to a significant and an extensively investigated compounds in chemical science. It has been derived through engineering mechanism at the molecular scale. The most important of these new materials are carbon nanotubes. Carbon nanosheets are 2-dimensional lattices of carbon nanotubes. To compute and study topological indices of nanostructures are a respected problem in nanotechnology. Quantitative structure-property and structure-activity relationships of the carbon nanotubes compounds necessitate expressions for the molecular topological features of these compounds. Topological indices are vital devices for investigating chemical compounds to comprehend the fundamental topology of chemical structures. Ev-degree and ve-degree based topological indices are two novel degrees based indices as of late defined in chemical graph theory. In this paper, we have computed topological indices based on ev-degree and ve-degree for the two significant classes of carbon nanosheets composed by C₄ and C₈ denoted by $T^1{C}_4{C}_8(S)[p,q]$ and $T^2{C}_4{C}_8(R)[p,q].$

Cancer is one of the most lethal diseases in humans and other species. Breast cancer is the second most frequent cancer after skin cancer, and it develops in the breast. The treatment recommendations are variable. The lack of appropriate medication has worsened the disease. Based on prior research, scientists are testing drugs based on medical therapies. Many drugs which include Abemaciclib, Thiotepa, Anastrozole, Tamoxifen, Abraxane, Capecitabine, Exemestane, and Ixabepilone are listed in the new recommendations. A topological index is a type of molecular descriptor that simply defines numerical values associated with the molecular structure of a compound that is effectively used in modeling many physicochemical properties in numerous quantitative structure-property relationship (QSPR) studies. In this study, several newly defined ve-degree of end vertices of each edge-based entropy indices for breast cancer drugs were investigated. A QSPR was established between entropy indices and the physical properties of breast cancer drugs to assess the efficacy of entropy indices. For the computation of entropy indices, a Maple-based algorithm was developed. The QSPR studies were obtained using the linear and cubic regression methods with the help of SPSS. The obtained results reveal that entropy indices under study have a strong correlation with the physical characteristics. Using simple linear regression, we analyzed that $EN{T}_{\mathit{ReZ}{G}_1}$ index is the best predictor of boiling point, enthalpy of vaporization, and molar volume, and $EN{T}_{R_{-1}}$ index is the best predictor of flash point, molar refraction and polarizability. Using cubic regression, we analyzed that the only augmented Zagreb entropy index predicts Melting Point.

Stokes flows of a Maxwell fluid produced by the motion of a wall are analyzed under the slip condition at the boundary. The wall is assumed to be translated in its plane with a given velocity. The relative velocity between the fluid at the wall and the wall is assumed to be proportional to the shear rate at the wall. The exact expressions for the velocity and shear stress are determined by means of a Laplace transform. The velocity fields corresponding to both slip and nonslip conditions for Maxwell and viscous Newtonian fluids are obtained. Two particular cases, namely sinusoidal oscillations and translation with a constant velocity of the wall, are studied. In the case of flows of a Maxwell fluid with a nonslip boundary condition, the velocity is discontinuous across a vortex sheet; this situation does not appear for flows with slip conditions. In this case, the velocity is always continuous. Because the exact expression for the velocity is rather complicated, two small-time and large-time expressions of the velocity are derived. Results for Maxwell fluids are compared with those of viscous Newtonian fluids in both cases of the flow with slip and nonslip conditions. Also, the exact and approximate solutions are compared and good agreement is found. In addition, the influence of the slip coefficient on the velocity and on the relative velocity is studied.

Quantitative structure-property and structure-activity relationships of the silicon carbide compounds necessitate expressions for the molecular topological features of these compounds. Topological indices are vital devices for investigating chemical compounds to comprehend the fundamental topology of chemical structures. Ev-degree and ve-degree based topological indices are two novel degrees based indices as of late defined in chemical graph theory. Ev-degree and ve-degree based topological indices have been defined as corresponding to their relating partners. In this article, we have computed degree based topological indices namely ev-degree Zagreb type index, ev-degree Randic index, ve-degree atom-bond connectivity index, ve-degree geometric-arithmetic index, ve-degree harmonic index, and ve degree sum-connectivity (ve-χ) based on ev-degree and ve-degree for silicon carbide Si₂C₃-II[p, q].