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 two issues in June 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

Computation of hosaya polynomial, wiener and hyper wiener index of jahangir graph \(j_{6,m}\)

JPRM-Vol. 1 (2017), Issue 1, pp. 30 – 40 Open Access Full-Text PDF
Mehdi Rezaei, Mohammad Reza Farahani, Waqas Khalid, Abdul Qudair Baig
Abstract: Let \(G = (V, E)\) be a simple connected graph with vertex set \(V\) and edge set \(E\). For two vertices \(u\) and \(v\) in a graph \(G\), the distance \(d(u, v)\) is the shortest path between \(u\) and \(v\) in \(G\). Graph theory has much advancements in the field of theoretical chemistry. Recently, chemical graph theory is becoming very popular among researchers because of its wide applications of mathematics in chemistry. One of the important distance based topological index is the Wiener index, defined as the sum of distances between all pairs of vertices of \(G\), defined as \(W(G) = \sum_{ u,v∈V (G)} d(u, v)\). The Hosaya polynomial is defined as \(H(G, x) =\sum _{u,v∈V (G)} x ^{d(u,v)}\). The hyper Wiener index is defined as \(WW(G) =\sum_{u,v∈V (G)} d(u, v) + \frac{1}{2}\sum_{u,v∈V (G)}d^{2}(u, v)\). In this paper, we study and compute Hosaya polynomial, Wiener index and hyper Wiener index for Jahangir graph \(J_{6,m}\), \(m ≥ 3\). Furthermore, we give exact values of these topological indices.
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Properties of co-intersection graph of submodules of a module

JPRM-Vol. 1 (2017), Issue 1, pp. 16 – 29 Open Access Full-Text PDF
Lotf Ali Mahdavi, Yahya Talebi
Abstract: Let \(R\) be a ring with identity and \(M\) be a unitary left Rmodule. The co-intersection graph of proper submodules of \(M, Ω(M)\) is an undirected simple graph whose vertices are non-trivial submodule of \(M\) in which two vertices N and K are joined by an edge, if and only if \(N + K \neq M\). In this paper, we study several properties of \(Ω(M)\). We prove that, if \(Ω(M)\) is a path, then \(Ω(M) \cong P_2 \)or \(Ω(M) \cong P_3\). We show that, if \(Ω(M)\) is a forest, then each component of \(Ω(M)\) is complete or star graph. We determine the conditions under which \(Ω(M)\) is weakly perfect. Moreover, we introduce the universal vertices and the dominating sets of \(Ω(M)\) and their relationship with the non-trivial small submodules of \(M\).
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Narumi-Katayama and modified Narumi-Katayama indices of graphs

JPRM-Vol. 1 (2017), Issue 1, pp. 08 – 15 Open Access Full-Text PDF
Mehdi Rezaei, Muhammad Sh. Sardar, Sohail Zafar, Mohammad R. Farahani.
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.
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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.
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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.
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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.
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Volume 20 (2024)

Volume 19 (2023)

Volume 18 (2022)

Volume 17 (2021)

Volume 16 (2020)

Volume 15 (2019)

Volume 14 (2018)

Volume 13 (2017)

Volume 12 (2016)

Volume 11 (2015)

Volume 10 (2014)

Volume 09 (2013)

Volume 08 (2012)

Volume 07 (2011)

Volume 06 (2010)

Volume 05 (2009)

Volume 04 (2008)

Volume 03 (2007)

Volume 02 (2006)

Volume 01 (2005)