# Journal of Prime Research in Mathematics

Journal of Prime Research in Mathematics (JPRM) ISSN: 1817-3462 (Online) 1818-5495 (Print) is an HEC recognized, Scopus indexed, open access journal which provides a plate forum to the international community all over the world to publish their work in mathematical sciences. JPRM is very much focused on timely processed publications keeping in view the high frequency of upcoming new ideas and make those new ideas readily available to our readers from all over the world for free of cost. Starting from 2020, we publish one Volume each year containing four issues in March, June, September and December. The accepted papers will be published online immediate in the running issue. All issues will be gathered in one volume which will be published in December of every year.

Latest Published Articles

### Narumi-Katayama and modified Narumi-Katayama indices of graphs

JPRM-Vol. 1 (2017), Issue 1, pp. 08 – 15 Open Access Full-Text PDF
Abstract: Let $$G$$ be a simple connected molecular graph in chemical graph theory, then its vertices correspond to the atoms and the edges to the bonds. Chemical graph theory is an important branch of graph theory, such that there exits many topological indices in it. Also, computing topological indices of molecular graphs is an important branch of chemical graph theory. Topological indices are numerical parameters of a molecular graph $$G$$ which characterize its topology. In the present study we compute and report several results of the Narumi-Katayama and modified NarumiKatayama indices for some widely used chemical molecular structures.

### Vertex equitable labeling for ladder and snake related graphs

JPRM-Vol. 1 (2017), Issue 1, pp. 01 – 07 Open Access Full-Text PDF
A. Lourdusamy, F. Patrick
Abstract: Let $$G$$ be a graph with p vertices and q edges and $$A = {0, 1, 2, · · · ,\frac{q}{2}}$$. A vertex labeling $$f : V (G) → A$$ induces an edge labeling $$f^∗$$ defined by $$f^∗ (uv) = f(u) + f(v)$$ for all edges $$uv$$. For $$a ∈ A$$, let $$v_f (a)$$ be the number of vertices $$v$$ with$$f(v) = a$$. A graph $$G$$ is said to be vertex equitable if there exists a vertex labeling f such that for all $$a$$ and $$b$$ in A, $$|v_f (a) − v_f (b)| ≤ 1$$ and the induced edge labels are $${1, 2, 3, · · · , q}$$. In this paper, we prove that triangular ladder $$T L_n, L_n ⊙ mK_1, Q_n ⊙ K_1, T L_n⊙K_1$$ and alternate triangular snake $$A(T_n)$$ are vertex equitable graphs.

### Rational cubic spirals

JPRM-Vol. 1 (2016), Issue 1, pp. 145 – 157 Open Access Full-Text PDF
Ayesha Shakeel, Maria Hussain, Malik Zawwar Hussain
Abstract: A parametric rational cubic approximation scheme is presented to preserve the monotone curvature profile of the given curve. The rational cubic curve has four control points and two free parameters. Values of control points are attained by $$C^1$$ -approximation. Simple sufficient data dependent constraints are obtained on the free parameters to preserve the monotonicity of curvature of given curve. Devised curvature-preserving approximation scheme is simple and robust.

### Combined effect of slip and radiation on MHD flow past a constantly moving vertical plate with variable temperature

JPRM-Vol. 1 (2016), Issue 1, pp. 130 – 144 Open Access Full-Text PDF
M. A. Imran, Shakila Sarwar, M. Imran, Maryam Aleem.
Abstract: The unsteady free convection of an MHD flow of a viscous fluid passing a vertical plate which is constantly moving with variable temperature is analyzed by taking slip and radiation into consideration. The dimensionless governing equations for temperature and velocity fields are solved using Laplace transform technique. The radiative and slip effects are taken into consideration and the whole system is rotating as a rigid body with a constant angular velocity about the z-axis. Exact solutions are obtained for the two components of velocity. Some known solutions from the literature are obtained as a limiting case. The obtained solutions satisfy the initial and boundary conditions. Some physical aspects of flow parameters on the fluid motion are graphically presented.

### Cartesian product of interval-valued fuzzy ideals in ordered semigroup

JPRM-Vol. 1 (2016), Issue 1, pp. 120 – 129 Open Access Full-Text PDF
Hidayat Ullah Khan, Asghar Khan, Nor Haniza Sarmin
Abstract: Interval-valued fuzzy set theory is a more generalized theory that can deal with real world problems more precisely than ordinary fuzzy set theory. In this paper, the concepts of interval-valued fuzzy (prime, semiprime) ideal and the Cartesian product of interval-valued fuzzy subsets have been introduced. Some interesting results about Cartesian product of interval-valued fuzzy ideals, interval-valued fuzzy prime ideals, intervalvalued fuzzy semiprime ideals, interval-valued fuzzy bi-ideals and intervalvalued fuzzy interior ideals in ordered semigroups are obtained. The purport of this paper is to link ordinary ideals with interval-valued fuzzy ideals by means of level subset of Cartesian product of interval-valued fuzzy subsets.

### A novel approach to approximate unsteady squeezing flow through porous medium

JPRM-Vol. 1 (2016), Issue 1, pp. 91 – 109 Open Access Full-Text PDF
Mubashir Qayyum, Hamid Khan, M.T. Rahim
Abstract: In this article, a new alteration of the Homotopy Perturbation Method (HPM) is proposed to approximate the solution of unsteady axisymmetric flow of Newtonian fluid. The flow is squeezed between two circular plates and passes through a porous medium channel. The alteration extends the Homotopy Perturbation with a Laplace transform, which is referred to as the Laplace Transform Homotopy Perturbation Method (LTHPM) in this manuscript. A single fourth order non-linear ordinary differential equation is obtained using similarity transformations. The resulting boundary value problem is then solved through LTHPM, HPM and fourth order Implicit Runge Kutta Method (IRK4). Convergence of the proposed scheme is checked by finding absolute residual errors of various order solutions. Also, the validity is confirmed by comparing numerical and analytical (LTHPM) solutions. The comparison of obtained residual errors shows that LTHPM is an effective scheme that can be applied to various initial and boundary value problems in science and engineering