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- Mobeen Munir, Waqas Nazeer, Shazia Rafique, Shin Min Kang
- Symmetry
- 2016

Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate… (More)

- Mobeen Munir, Waqas Nazeer, Zakia Shahzadi, Shin Min Kang
- Symmetry
- 2016

Mobeen Munir 1, Waqas Nazeer 1, Zakia Shahzadi 1 and Shin Min Kang 2,3,* 1 Division of Science and Technology, University of Education, Lahore 54000, Pakistan; mmunir@ue.edu.pk (M.M.); nazeer.waqas@ue.edu.pk (W.N.); zakiashahzadi@yahoo.com (Z.S.) 2 Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju… (More)

- Mobeen Munir, Waqas Nazeer, Shazia Rafique, Abdul Rauf Nizami, Shin Min Kang
- Symmetry
- 2017

The recent discovery of boron triangular nanotubes competes with carbon in many respects. The closed form of M-polynomial of nanotubes produces closed forms of many degree-based topological indices which are numerical parameters of the structure and, in combination, determine properties of the concerned nanotubes. In this report, we give M-polynomials of… (More)

- Mobeen Munir, Waqas Nazeer, Shazia Rafique, Shin Min Kang
- Symmetry
- 2016

Mobeen Munir 1, Waqas Nazeer 1, Shazia Rafique 2 and Shin Min Kang 3,4,* 1 Division of Science and Technology, University of Education, Lahore 54000, Pakistan; mmunir@ue.edu.pk (M.M.); nazeer.waqas@ue.edu.pk (W.N.) 2 Center for Excellence in Molecular Biology, Punjab University Lahore, Lahore 53700, Pakistan; shaziarafique@gmail.com 3 Department of… (More)

1 Department of Mathematics, Govt. College Kamoke, Gujranwala, Pakistan 2 Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan 3 Division of Science and Technology, University of Education, Lahore, Pakistan E-mail: arhamusman2001@gmail.com, saeedkhan07@live.com, waqaster@yahoo.com , tanveer.7955180@yahoo.com. ABSTRACT: In this… (More)

1 Department of Mathematics, Lahore College for Women University, Lahore-Pakistan E-mail: imrana.kousar@hotmail.com 2 Department of Mathematics, Lahore College for Women University, Lahore-Pakistan E-mail: saimanazeer123@yahoo.com 3* Division of Science and Technology, University of Education, Township Lahore-Pakistan E-mail: waqaster@yahoo.com ABSTRACT:… (More)

- Sun Young Cho, Abdul Aziz Shahid, Waqas Nazeer, Shin Min Kang
- SpringerPlus
- 2016

In this note, we give fixed point results in fractal generation (Julia sets and Mandelbrot sets) by using Noor iteration scheme with s-convexity. Researchers have already presented fixed point results in Mann and Ishikawa orbits that are examples of one-step and two-step feedback processes respectively. In this paper we present fixed point results in Noor… (More)

- Shin Min Kang, Saima Nazeer, +5 authors A. Rafiq
- 2014

Abstract A multilevel distance labeling of the graph G is a function f = (V (G),E(G)) on V (G) of G into N ∪ {0} so that |f(u) − f(v)| ≥ diam(G) + 1− d(u, v) for all u, v ∈ V (G). The smallest span taken over all multilevel distance labeling of G is radio number rn(G) of G. In this paper, we completely determine the radio number rn(G) of G where G is the… (More)

- Muhammad Ajmal, Waqas Nazeer, Mobeen Munir, Shin Min Kang, Young Chel Kwun
- Symmetry
- 2017

Muhammad Ajmal 1, Waqas Nazeer 2, Mobeen Munir 2, Shin Min Kang 3,4 and Young Chel Kwun 5,* 1 Department of Mathematics, Government Muhammdan Anglo Orintal College, Lahore 54000, Pakistan; majmalkhan82@gmail.com 2 Division of Science and Technology, University of Education, Lahore 54000, Pakistan; nazeer.waqas@ue.edu.pk (W.N.); mmunir@ue.edu.pk (M.M.) 3… (More)

- Young Chel Kwun, Mobeen Munir, Waqas Nazeer, Shazia Rafique, Shin Min Kang
- Scientific reports
- 2017

V-Phenylenic nanotubes and nanotori are most comprehensively studied nanostructures due to widespread applications in the production of catalytic, gas-sensing and corrosion-resistant materials. Representing chemical compounds with M-polynomial is a recent idea and it produces nice formulas of degree-based topological indices which correlate chemical… (More)