Applied Mathematics

A graph G=(V,E) with n vertices is said to be admitted prime labeling if its vertices can be labeled with distinct positive integers not exceeding n such that the label of each pair of adjacent vertices are relatively prime. Some previous work on prime labeling includes prime labeling of bipartite graphs and ladder graphs. In this work, a new graph called Snow graph which is a union of wheel and star graphs is introduced. A theorem is given to obtain a prime labeling for this graph and an algorithm for prime labeling is given.

In this paper, we expanded the application of Shehu transformation to obtained the solution for system of ordinary differential equations that subjected to known or unknown initial conditions, which applies in calculation for the cost of activity.

The group B(m,n) satis?es identity relation x^n = 1. Moreover, sinceF_m^n is a verbal subgroup of group F^m generated with word x^n, the group B(m,n) is free in the variety of all n-periodic groups, i.e. all groups, where the identical relationx^n = 1holds. The group B(m,n) is free in the variety of all n-periodical groups and is called free-periodical or free Burnside group of the period n and rank m.

In 2019, Matiama presented a new integral transformation called Shehu transformation, which used to solve many types of differential equations. In this article, we obtained the derivation and integration of Shehu transformation with its applications.

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In this paper, A survey on the use of the Haar wavelet method to solve linear and nonlinear integral equations (Volterra, Fredholm, integro-differential equations) is presented. Also, the investigation of Haar wavelet method for solving singular integral equations is presented. Review shows that the Haar wavelet method is efficient and powerful in solving wide class of linear and nonlinear integral equations.

A two-dimensional laminar unsteady MHD free convective heat and mass transfer flow past a vertical porous plate immersed in a porous medium has been studied numerically in presence of chemical reaction, heat generation and variable suction. The governing partial differential equations are reduced to a system of self-similar equations using the similarity transformations. The resultant equations are then solved numerically using the Runge-Kutta method along with shooting technique. The effects of governing physical parameters on velocity, temperature and concentration as well as skin-friction coefficient, Nusselt number and Sherwood number are computed and presented in graphical and tabular forms. Comparisons with previously published work are performed and the results are found to be in excellent agreement.

The goal objective of this study is to propose a new double ARA transform (DARAT). We employ this transform to prove the convolution, existence and other relevant theorems as well as derivatives properties. Subsequently, this transform is applied to solve some illustrative integral- differential equations. This approach was shown to be a powerful and efficient means to tack integral- differential equations.

Present paper is an important study for constructing magic squares of odd orders. This magic squares have been formed using the properties of Latin squares. Here, reduced Latin square is used and it is formulated by using the cyclic shifting method with the entries (????, ????,...., ????) (????(????- ????),.... ???? power ???? ).This work has been generalized for magic square of order ???? power ????, when ???? is odd and ???? by using the mathematical formula ?????????(???????????? ???? power ????): ????= ????, ????,..., ???? power ????. The method is tested for ????, ???? power ???? and ????.

The magnetic response of transverse wave propagation of double layered nanoplate embedded in an elastic medium is studied employing nonlocal continuum theory. The displacement equation of nanoplate with magnetic and elastic medium is devised with the help of Lorentz force and Winkler elastic foundation. The frequency equations are acquired for nanoplate with simply supported edges. The numerical result reveals that the magnetic strength and elastic medium increases the frequencies of double layered nanoplates. The perfection of the present frequency value is noted by comparing it with the existing literature.

The Line graph L(G) of an undirected graph G is another graph L(G) that represents the find adjacencies between the edges of G. In this paper, we find the Maximum and Minimum of total coloring for a certain Line graphs of a snake graph families and further we established the results on maximum number colors required to total coloring to the graph G is denoted by and similarly we color the vertex of a snake graph and obtained certain results and denoted by X_Max^(G)