# 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

### K Banhatti and k hyper banhatti indices of the line graphs of h-pantacenic nanotubes

JPRM-Vol. 1 (2018), Issue 1, pp. 62 – 73 Open Access Full-Text PDF
Abdur Rehman, Muhammad Nawaz, Waqas Nazeer, Wei Gao
Abstract: Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structureactivity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. The aim of this report is to compute the first and second K Banhatti indices of the Line Graphs of H-Pantacenic Nanotubes. We also compute the first and second K hyper Banhatti indices of the Line Graphs of H-Pantacenic Nanotubes.

### Bounds of F-index for unicyclic graphs with fixed pendent vertices

JPRM-Vol. 1 (2018), Issue 1, pp. 51 – 61 Open Access Full-Text PDF
M. Javaid, Maqsood Ahmad, M. Hussain, W.C. Teh
Abstract: Furtula and Gutman [J. Math. Chem., 53 (4) (2015), 1184- 1190] reinvestigated the $$F$$-index as a sum of cubes of the degrees of all the vertices in a chemical graph and proved its various properties. A connected graph with equal order and size is called unicyclic graph, where order is number of vertices and size is number of edges. In this paper, we characterize the extremal graphs in a family of graphs called by unicyclic graphs with fixed number of pendent vertices. We also investigate the bound on $$F$$-index in the same family of graphs i.e $$4(2n + 3α) ≤ F(G) ≤ 8n + α(α + 2)(α + 3)$$ for each $$G ∈ \mathcal{U}_{n}^{ α}$$, where $$\mathcal{U}_{n}^{ α}$$ is a class of all the unicyclic graphs such that the order of each graph is $$n$$ with $$α$$ pendent vertices.

### A new paradigm for increasing the continuity of subdivision schemes

JPRM-Vol. 1 (2018), Issue 1, pp. 37 – 50 Open Access Full-Text PDF
Abstract: Subdivision schemes having high continuity are always required for designing of smooth curves and surfaces. In this paper, we present a paradigm to generate a family of binary approximating subdivision schemes with high continuity based on probability distribution. The analysis and convexity preservation of some members of the family are also presented. Subdivision schemes give skewed behavior on convex data due to probability parameter.

### New twelfth order algorithms for solving nonlinear equations by using variational iteration technique

JPRM-Vol. 1 (2018), Issue 1, pp. 24 – 36 Open Access Full-Text PDF
Muhammad Nawaz, Amir Naseem, Waqas Nazeer
Abstract: In this paper, we proposed three new algorithms for solving non-linear equations by using variational iteration technique. We discuss the convergence criteria of our newly developed algorithms. To demonstrate the efficiency and performance of these methods, several numerical examples are given which show that our generated methods are best as compared to Newton’s method, Halley’s method, Househ¨older’s method and other well known iterative methods. The variational iteration technique can be used to suggest a wide class of new iterative methods for solving a system of non-linear equations.

### Invariance of metric dimension of subdivision of the crown graph

JPRM-Vol. 1 (2018), Issue 1, pp. 18 – 23 Open Access Full-Text PDF
Abdul Rauf Nizami
Abstract: Metric dimension has applications in several areas including computer navigation, chemistry, and image processing. In this paper we give metric dimension of the crown graph $$S_n$$, $$n ≥ 3$$, and show that it remains invariant under any of its subdivision.

### Generalized $$\xi$$-rings

JPRM-Vol. 1 (2018), Issue 1, pp. 13 – 17 Open Access Full-Text PDF
Peter V. Danchev
Abstract: Let $$R$$ be a ring with center $$C(R)$$. A ring $$R$$ is called a ξring if, for any element $$x ∈ R$$, there exists an element $$y ∈ R$$ such that $$x − x^2y ∈ C(R)$$. In Proc. Japan Acad. Sci., Ser. A – Math. (1957), Utumi describes the structure of these rings as a natural generalization of the classical strongly regular rings, that are rings for which $$x = x^2 y$$. In order to make up a natural connection of $$ξ$$-rings with the more general class of von Neumann regular rings, that are rings for which $$x =xyx$$, we introduce here the so-called generalized $$ξ$$-rings as those rings in which $$x − xyx ∈ C(R)$$. Several characteristic properties of this newly defined class are proved, which extend the corresponding ones established by Utumi in these Proceedings (1957).