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Dr. Rashid Farooq
Assistant Professor
Department of Mathematics

SNS
National University of Sciences and Technology (NUST)
H-12, Islamabad
Tel : +92 51 9085 5580
Email : farooq (at mark) sns.nust.edu.pk

Specialization
Combinatorial Optimization, Spectral Graph Theory

Education
D.Sc. Mathematics (Kyoto University, Japan)

 
Education:
 
  • 1996-1998: Master of Science, Quaid-i-Azam University, Islamabad Pakistan. 
  • 1998-2000: Master of Philosophy, Quaid-i-Azam University, Islamabad Pakistan. 
  • 2003-2007: Doctor of Science (Supervised by  Prof. Satoru Fujishige), Kyoto University, Japan.
 
Positions Held:
 
• October 01, 2012-date: Head of Department (Mathematics)
   National University of Sciences and Technology, Islamabad, Pakistan
• May, 2007- date: Assistant Professor
   National University of Sciences and Technology, Islamabad, Pakistan
• March, 1999-February, 2001: Teaching Assistant
   Institute of Business Administration and Technology Islamabad, Pakistan.

Research Interests:

My recent interest is in Spectral Graph Theory. More precisely, I work on Energy of Graphs and Digraphs, and Topological Indices. Moreover, I also work in Game Theory, specially, in Two-sided Matching Markets problems.

Research Students

PhD

  • ​Dr Yasir Ali                 2007-2011
  • Mr Mehar Ali Malik         2012-present
  • Mr Mehtab Khan            2013-present
  • Ms. Shehnaz Akhter        2015-present
  • Ms. Sumaira Hafeez        2015-present


MPhil

  • Sabeel-e-Hafi                                 2015-present
  • Fatima Farrrukh                               2015 – present
  • Nazia Nazir                                    2015- 2016
  • Mr. Yasir Masood                              2014- 2015
  • Ms Zarmina Zaman Babar                      2013-2014
  • Ms Qudsia Noureen                            2013-2014
  • Ms. Ayesha Mahmood                     2011-2013
  • Ms Sumbul Azeem                       2011-2013               
  • Mr. M. Usman Ali                       2011-2013  (Co-Supervisor)


Foreign Research Visits

  • Keio University, Yokohama Japan (July 2 ~ August 24, 2009). (Sponsored by Global COE, Kyoto University)
  • Keio University, Yokohama Japan (June 19 ~ September 06, 2010). (Sponsored by Japan Students Services Organization- JASSO)
  • Abdus Salam International Centre for Theoretical Physics, Trieste Italy (September 2012). (Sponsored by NUST and AS-ICTP)
 

 

                         

Research ​Publications:
 
​S/No ​Title
​28. ​Zahid Iqbal, Muhammad Ishaq, Rashid Farooq; Computing different versions of atom-bond connectivity index of dendrimers, Journal Of Informatics And Mathematical Sciences, (to appear)
​27. ​R. Farooq, A. Mahmood;  A note on a two-sided discrete-concave market with possibly bounded salaries, International Game Theory Review, Vol. 19, No. 3, (2017) pp: 1750017-1 -- 1750017-21.
​26. ​Fatima Farrukh, Rashid Farooq and Mohammad Reza Farahani: On the atom-bond connectivity and geometric-arithmetic indices of SiO2 layer structure, Moroccan Journal of Chemistry, Vol. 5 No. 2 (2017) 384-390.
​25. ​M. Khan, R. Farooq; On the energy of bicyclic signed digraphs, Journal of Mathematical Inequalities, Vol. 11, No. 3 (2017), 845–862.
​24. ​R. Farooq, M. Khan, F. Ahmad:  Extremal iota energy of bicyclic digraphs, Applied Mathematics and Computation, 303 (2017) 24–33.​
​23. ​M. A. Malik, R. Farooq: Computing topological indices of some hyper-branched macromolecules, Journal of Optoelectronics and Advanced Materials, Vol. 18, No. 11-12, 2016, 1057 – 1068.
​22. ​S. Akhter, R. Farooq: Computing bounds for the general sum-connectivity index of some graph operations, Algebra and discrete mathematics (to appear). 
​21. ​M. Khan, R. Farooq, J. Rada: Complex adjacency matrix and energy of digraphs, Linear Multilinear Algebra, http://dx.doi.org/10.1080/03081087.2016.1265064 
​20. ​Fatima Farrukh,  Sabeel-e-Hafi, Rashid Farooq, Mohammad R. Farahani; Calculating some topological indices of SiO2 layer structure, Journal Of Informatics And Mathematical Sciences, Vol. 8, No. 3, pp. 181–187, 2016
​19. ​W. Gao, W. F. Wang, M. K. Jamil, R. Farooq, M. R. Farahani:  Generalized atom-bond connectivity analysis of several chemical molecular graphs, Bulgarian Chemical Communications, Vol. 48, Number 3 (pp. 543 - 549) 2016.
​18. ​R. Farooq, M. A. Malik, Q. Naureen and S. Pirzada, On the nullity of a family of tripartite graphs,  Acta Univ. Sapientiae, Informatica,  Vol. 8(1), pp. 96–107, (2016)
​17. ​Nazia Nazir, R. Farooq,  Mehar Ali Malik: Computing some degree-based topological indices of a heterofunctional dendrimer, Journal of Optoelectronics and Advanced Materials, Vol. 18, Iss. 5-6, May – June 2016, p. 574 - 586
​16. M. A. Malik, R. Farooq; On the eccentric-connectivity index of some 3-fence graphs and their line graphs,International Journal of Applied and Computational Mathematics (to appear)​
​15. R. F​arooq, M. Khan, Y. Masood; Extremal energy of digraphs, Kragujevac Journal of Mathematics, Vol 40(1) P 79–89, 2016​.
​14. ​R. Farooq, N. Nazir, M. A. Malik, M. Arfan; Eccentricity based topological indices of a hetrofunctional dendrimer, Journal of Optoelectronics and Advanced Materials, Vol. 17, No. 11-12,  pp. 1799 – 1807, 2015.
​13.
R. Farooq, M. A. Malik; On some eccentricity based topological indices of nanostar dendrimers, Optoelectronics and Advanced Materials-Rapid Communications;  Vol. 9, No. 5-6, pp. 842—849, 2015​.
​12. ​M. A. Malik, R. Farooq; Some conjectures on energy and Estrada index of CNCk[n] nanocones, Optoelectronics and Advanced Materials-Rapid Communications;  Vol. 9, No. 3-4, pp. 415 – 418, 2015.
11​. ​M. A. Malik, R. Farooq; Computational results on the energy and Estrada index of TUC4C8(R)[m, n] nanotubes, Optoelectronics and Advanced Materials-Rapid Communications, Vol. 9, No. 1-2, pp. 311-313, 2015.
​10. Sumbul Azeem, R. Farooq; M^{\natural}-convexity and Ultramodularity on Integer Lattice; Mathematical Inequalities and Applications; Vol. 18, Number 3, pp. 949—958,  2015.
​9. ​M. Khan, R. Farooq, A.A. Siddiqui, On the extremal energy of bicyclic digraphs; Journal of Mathematical Inequalities, Vol. 9, Number 3, pp. 799—810, 2015.
​8. R. Farooq, T. Fleiner, A. Tamura; Matching with partially ordered contracts; Japan Journal of Industrial and Applied Mathematics, Vol. 29, pp. 401-417, 2012 
​7. Y. Ali, R. Farooq; Existence of stable outcome in a job market with linear valuations and possibly bounded salaries; Pacific Journal of Optimization, Vol. 7, No.3, pp.531-550, 2011.
​6. Y. Ali, R. Farooq; Pairwise stability in a two-sided matching market with indivisible goods and money; Journal of Operations Research Society of Japan,  Vol. 54, No. 1, pp.1-11, 2011.
​5. R. Farooq; A polynomial-time algorithm for a stable matching problem with linear valuations and bounded side payments; Japan Journal of Industrial and Applied Mathematics, Vol. 25, No 1, pp. 83-89,  2008.
​4. R. Farooq, Y.T. Ikebe, A. Tamura; On labor allocation model with possibly bounded salaries; Journal of Operations Research Society of Japan, Vol. 51, No 2, pp. 136-154,  2008.
​3. R. Farooq, A. Shioura; A note on the equivalence between substitutability and M^{n}-convexity; Pacific Journal of Optimization, Vol. 1, No 1, pp. 243-252, January 2005.
​2. R. Farooq, A. Tamura; A new characterization of M^{n}-convex set functions by substitutability; Journal of Operations Research Society of Japan, Vol. 47, No 1, pp. 18-24, 2004.
​1. A. Ali, R. Farooq; A note on finite metabelian groups of wielandt length two; Southeast Asian Bulletin of Mathematics, Vol. 25, pp. 187-190, 2001.
 

Current Courses:

  • Abstract Algebra

Previous Courses:

  • Number Theory
  • Graph Theory
  • Optimization Theory
  • Functional Analysis
  • Real Analysis
  • Linear Algebra
  • Metric and Topological Spaces