# 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

### Quasi invo-regular rings

JPRM-Vol. 1 (2019), Issue 1, pp. 01 – 04 Open Access Full-Text PDF
Peter V. Danchev
Abstract: We define the class of quasi invo-regular rings and prove that they curiously coincide with the so-called invo-regular rings, recently introduced and explored by the present author in Ann. Univ. Mariae CurieSklodowska – Sect. Math. (2018).

### Connective eccentricity index of certain path-thorn graphs

JPRM-Vol. 14 (2018), Issue 1, pp. 87 – 99 Open Access Full-Text PDF
M. Javaid, M. Ibraheem, A. A. Bhatti
Abstract: Let $$G$$ be a simple connected graph with $$V (G)$$ and $$E(G)$$ as the vertex set and edge set respectively. A topological index is a numeric quantity by which we can characterize the whole structure of a molecular graph or a network to predict the physical or chemical activities of the involved chemical compounds in the molecular graph or network. The connective eccentricity index of the graph $$G$$ is defined as $$ξ^{ce}(G) = \sum_{v∈G}\frac{d(v)}{e(v)}$$, where $$d(v)$$ and $$e(v)$$ denote the degree and eccentricity of the vertex $$v ∈ G$$ respectively. In this paper, we compute the connective eccentricity index of the various families of the path-thorn graphs and present the obtained results with the help of suitable mathematical expressions consisting on various summations. More precisely, the computed results are general extensions of the some known results.

### Solving differential equations by wavelet transform method based on the mother wavelets & differential invariants

JPRM-Vol. 14 (2018), Issue 1, pp. 74 – 86 Open Access Full-Text PDF
Hamid Reza Yazdani, Mehdi Nadjafikhah, Megerdich Toomanian
Abstract: Nowadays, wavelets have been widely used in various fields of science and technology. Meanwhile, the wavelet transforms and the generation of new Mother wavelets are noteworthy. In this paper, we generate new Mother wavelets and analyze the differential equations by using of their corresponding wavelet transforms. This method by Mother wavelets and the corresponding wavelet transforms produces analytical solutions for PDEs and ODEs.

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

JPRM-Vol. 14 (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. 14 (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. 14 (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.