In this paper we give explicit formulas of the Kauffman bracket of the 2-strand braid link \(\widehat{x_{1}^{n}}\) and the 3-strand braid link \(\widehat{x_{1}^{b}x_{2}^{m}}\). We also show that the Kauffman bracket of the 3-strand braid link \(\widehat{x_{1}^{b}x_{2}^{m}}\) is actually the product of the Kauffman brackets of the 2-strand braid links \(\widehat{x_{1}^{b}}\) and \(\widehat{x_{1}^{m}}\).

A topological index is a real number related to a molecular graph, which is a graph invariant. Uptill now there are several topological indices are defined. Some of them are distance based while the others are degree based, all have found numerous applications in pharmacy, theoretical chemistry and especially in QSPR/QSAR research. In this paper, we compute some degree based topological indices i.e some versions of Zagreb indices, Randic index, General sum connectivity index and GA index of Hex board and of its line graph.

In this paper the velocity field and the adequate shear stress corresponding to the rotational flow of a fractional Maxwell fluid, between two infinite coaxial circular cylinders with inner cylinder is at rest and outer is moving, are determined by applying the Laplace and finite Hankel transforms. The solutions that have been obtained are presented in terms of generalized G functions. The expressions for the velocity field and the shear stress are in the most simplified form. Moreover, these solutions satisfy both the governing differential equation and all imposed initial and boundary conditions. The corresponding solutions for ordinary Maxwell and Newtonian fluids are recovered as limiting cases of general solutions.

Let \(G=(V,E)\) be a simple connected graph. The sets of vertices and edges of \(G\) are denoted by \(V=V(G)\) and \(E=E(G)\), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. In chemical graph theory, we have many topological indices for a molecular graph. The First and Second Zagreb indices are equal to \(M_1(G)=\sum_{uv \in E(G)}[d_u+d_v]\) and \(M_2(G)=\sum_{uv \in E(G)} d_{u}d_{v}\), respectively. In this paper, we focus on the structure of Capra-designed planar benzenoid series \(Ca_k(C_6)\) \((k\geq0)\), and compute its Generalized Zagreb index.

We discuss the interacting QCD ghost dark energy with cold dark matter in the framework of Fractal cosmology. We investigate the cosmological parameters such as Hubble parameter, deceleration parameter and equation of state. We also discuss the physical significance of various cosmological planes like \(\omega_{D}-{\omega}’_{D}\) and state-finder. At the end, it is observed that all the results are compatible with observational data.

In this paper, we suggest and analyze two new algorithm of fourth and fifth order convergence. We rewrite nonlinear equation as an equivalent coupled system and then use modified decomposition technique to develop our algorithms. Convergence analysis of newly introduced algorithms has been discussed. To see efficiency and performance of these algorithms, we have made comparison of these algorithms with some well known algorithms existing in literature.

In this work, we investigate the process of accretion for static spherical symmetric geometries for isotropic fluid. For analyze this process we use the nonminimal magnetically charged regular black holes. For this purpose, we obtain generalized expressions for the accretion rate \(\dot{M}\), critical radius \(r_s\), critical speed \(v^2_s\) and squared sound speed \(c^2_s\) during the accretion process near the regular black holes. Finally, we study the behavior of radial velocity, energy density and rate of change of mass for each
regular black hole by plotting graph.

The fractional calculus approach is used in the constitutive relationship model of fractional Maxwell fluid. Exact solutions for the velocity field and the adequate shear stress corresponding to the rotational flow of a fractional Maxwell fluid, between two infinite coaxial circular cylinders, are obtained by using the Laplace transform and finite Hankel transform for fractional calculus. The solutions that have been obtained are presented in terms of generalized \(G_{b, c, d}(\cdot, t)\) and \(R_{b, c}(\cdot, t)\) functions. In the limiting cases, the corresponding solutions for ordinary Maxwell and Newtonian fluids are obtained from our general solutions. Furthermore, the solutions for the motion between the cylinders, when one of them is at rest, are also obtained as special cases from our results. Finally, the influence of the material parameters on the fluid motion is underlined by graphical illustrations.