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

Vertex-to-clique detour distance in graphs

JPRM-Vol. 1 (2016), Issue 1, pp. 45 – 59 Open Access Full-Text PDF
I. Keerthi Asir, S. Athisayanathan
Abstract: Let \(v\) be a vertex and \(C\) a clique in a connected graph \(G\). A vertex-to-clique \(u − C\) path P is a \(u − v\) path, where v is a vertex in \(C\) such that \(P\) contains no vertices of \(C\) other than \(v\). The vertex-to-clique distance, \(d(u, C)\) is the length of a smallest \(u−C\) path in \(G\). A \(u−C\) path of length \(d(u, C)\) is called a \(u − C\) geodesic. The vertex-to-clique eccentricity \(e_1(u)\) of a vertex \(u\) in \(G\) is the maximum vertex-to-clique distance from \(u\) to a clique \(C ∈ ζ\), where \(ζ\) is the set of all cliques in \(G\). The vertex-to-clique radius \(r_1\) of \(G\) is the minimum vertex-to-clique eccentricity among the vertices of \(G\), while the vertex-to-clique diameter \(d_1\) of \(G\) is the maximum vertex-to-clique eccentricity among the vertices of \(G\). Also the vertex toclique detour distance, \(D(u, C)\) is the length of a longest \(u−C\) path in \(G\). A \(u−C\) path of length \(D(u, C)\) is called a \(u−C\) detour. The vertex-to-clique detour eccentricity \(e_{D1}(u)\) of a vertex \(u\) in \(G\) is the maximum vertex-toclique detour distance from u to a clique \(C ∈ ζ\) in \(G\). The vertex-to-clique detour radius \(R_1\) of \(G\) is the minimum vertex-to-clique detour eccentricity among the vertices of \(G\), while the vertex-to-clique detour diameter \(D_1\) of \(G\) is the maximum vertex-to-clique detour eccentricity among the vertices of \(G\). It is shown that \(R_1 ≤ D_1\) for every connected graph \(G\) and that every two positive integers a and b with \(2 ≤ a ≤ b\) are realizable as the vertex-to-clique detour radius and the vertex-to-clique detour diameter, respectively, of some connected graph. Also it is shown that for any three positive integers \(a\), \(b\), \(c\) with \(2 ≤ a ≤ b < c\), there exists a connected graph G such that \(r_1 = a\), \(R_1 = b\), \(R = c\) and for any three positive integers \(a\), \(b\), \(c\) with \(2 ≤ a ≤ b < c\) and \(a + c ≤ 2b\), there exists a connected graph \(G\) such that \(d_1 = a\), \(D_1 = b\), \(D = c\).
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The t-pebbling number of some wheel related graphs

JPRM-Vol. 1 (2016), Issue 1, pp. 35 – 44 Open Access Full-Text PDF
A. Lourdusamy, F. Patrick, T. Mathivanan
Abstract: Let \(G\) be a graph and some pebbles are distributed on its vertices. A pebbling move (step) consists of removing two pebbles from one vertex, throwing one pebble away, and moving the other pebble to an adjacent vertex. The t-pebbling number of a graph \(G\) is the least integer \(m\) such that from any distribution of m pebbles on the vertices of \(G\), we can move t pebbles to any specified vertex by a sequence of pebbling moves. In this paper, we determine the t-pebbling number of some wheel related graphs.
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Projective configurations and the variant of cathelineaus complex

JPRM-Vol. 1 (2016), Issue 1, pp. 24 – 34 Open Access Full-Text PDF
Sadaqat Hussain, Raziuddin Siddiqui
Abstract: In this paper we try to connect the Grassmannian subcomplex defined over the projective differential map \(\acute{d}\) and the variant of Cathelineau’s complex. To do this we define some morphisms over the configuration space for both weight 2 and 3. we also prove the commutativity of corresponding diagrams.
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g-noncommuting graph of some finite groups

JPRM-Vol. 1 (2016), Issue 1, pp. 16 – 23 Open Access Full-Text PDF
M. Nasiri, A. Erfanian, M. Ganjali, A. Jafarzadeh
Abstract: Let \(G\) be a finite non-abelian group and \(g\) a fixed element of \(G\). In 2014, Tolue et al. introduced the g-noncommuting graph of \(G\), which was denoted by \(Γ^{g}_G\) with vertex set \(G\) and two distinct vertices \(x\) and \(y\) join by an edge if \([x, y] \neq g\) and \(g^{−1}\). In this paper, we consider induced subgraph of \(Γ^{g}_{G}\) on \(G /Z(G)\) and survey some graph theoretical properties like connectivity, the chromatic and independence numbers of this graph associated to symmetric, alternating and dihedral groups.
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A note on self-dual AG-groupoids

JPRM-Vol. 1 (2016), Issue 1, pp. 01 – 15 Open Access Full-Text PDF
Aziz-Ul-Hakim, I. Ahmad, M. Shah
Abstract: In this paper, we enumerate self-dual AG-groupoids up to order 6, and classify them on the basis of commutativity and associativity. A self-dual AG-groupoid-test is introduced to check an arbitrary AG-groupoid for a self-dual AG-groupoid. We also respond to an open problem regarding cancellativity of an element in an AG-groupoid. Some features of ideals in self-dual AG-groupoids are explored. Some desired algebraic structures are constructed from the known ones subject to certain conditions and some subclasses of self-dual AG-groupoids are introduced.
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On the mixed hodge structure associated hypersurface singularities

JPRM-Vol. 1 (2015), Issue 1, pp. 137 – 161 Open Access Full-Text PDF
Mohammad Reza Rahmati
Abstract: Let \(f : \mathbb{C}^{n+1} → \mathbb{C}\) be a germ of hypersurface with isolated singularity. One can associate to f a polarized variation of mixed Hodge structure \(H\) over the punctured disc, where the Hodge filtration is the limit Hodge filtration of W. Schmid and J. Steenbrink. By the work of M. Saito and P. Deligne the VMHS associated to cohomologies of the fibers of \(f\) can be extended over the degenerate point \(0\) of disc. The new fiber obtained in this way is isomorphic to the module of relative differentials of \(f\) denoted \(Ω_f\) . A mixed Hodge structure can be defined on \(Ω_f\) in this way. The polarization on \mathcal{H} deforms to Grothendieck residue pairing modified by a varying sign on the Hodge graded pieces in this process. This also proves the existence of a Riemann-Hodge bilinear relation for Grothendieck pairing and allow to calculate the Hodge signature of Grothendieck pairing.
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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)