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Dr. Rashid Farooq
Associate Professor
Department of Mathematics

National University of Sciences and Technology (NUST)
H-12, Islamabad
Tel : +92 51 9085 5550
Email : farooq (at mark)

Combinatorial Optimization, Spectral Graph Theory

Doctor of Science, Kyoto University, Japan,     Master of Philosophy,Quaid-i-Azam University, Islamabad, Pakistan, Master of Science, Quaid-i-Azam University, Islamabad, Pakistan , Bachelor of Science, Bahauddin Zakariya University, Multan, Pakistan

Dr. Rashid Farooq joined the Research Institute for Mathematical Sciences (RIMS), a research institute at Kyoto University, Japan, as a Research student in April 2002. He joined the doctoral programme of RIMS in April 2003 and earned Doctor of Science degree in Mathematics in March 2007. Soon after the completion of his doctoral degree, he joined NUST in May 2007.

Dr. Rashid Farooq has numerous research papers to his credit in the area of graph theory and game theory. He has supervised several doctoral and master students. His recent research interests include spectral graph theory and metric graph theory. Dr. Rashid was appointed as Head of Mathematics Department in October 2012 for a period of 3 years. In October 2018, he assumed the charge of Head of Mathematics Department for the second time. In June 2019, he took charge of the NUST School of Natural Sciences as Principal.

Recent research interests of Dr Rashid include spectral graph theory and metric graph theory. In particular, he works on energy of graphs and digraphs, topological indices, metric and strong metric dimension of graphs.

Research ​Publications:
​S/No ​Title
​36. ​S. Akhter, R. Farooq: Computing the eccentric connectivity index and eccentric adjacency index of conjugated trees, Utilitas Mathematica (to appear)​
​35. ​S. Akhter, R. Farooq: Metric dimension of fullerene graphs, Electronic Journal of Graph Theory and Applications (to appear)
​34. ​S. Akhter, R. Farooq: On the eccentric adjacency index of unicyclic graphs and trees, Asian-European Journal of Mathematics (to appear)
​33. ​Naila Mehreen, R. Farooq, Shehnaz Akhter: On partition dimension of fullerene graphs, AIMS Mathematics, 3(3), 343-352 (2018).
​32. ​S. Hafeez, R. Farooq, M. Khan: Bicyclic signed digraphs with maximal energy, Applied Mathematics and Computation, 347, 702–711 (2019)
​31. S. Akhter, R. Farooq, S. Pirzada; Exact formulae of general sum-connectivity index for some graph operations, MATEMATIČKI VESNIK, 70(3)  (2018), 267-282.
​30. R. Farooq, Mehtab Khan and Sarah Chand, On iota energy of signed digraphs, Linear and  Multilinear Algebra, VOL.67, NO.4,705–724 (2019)
​29. Rashid Farooq, Sarah Chand and Mehtab Khan, On iota energy of bicyclic signed digraphs,  Asian-European Journal of Mathematics (
​28. ​Zahid Iqbal, Muhammad Ishaq, Rashid Farooq; Computing different versions of atom-bond connectivity index of dendrimers, Journal Of Informatics And Mathematical Sciences, Vol. 9, No. 1, pp. 217–229, 2017
​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, 
​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.
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.

Taught following courses at undergraduate and postgraduate level:

  • Operations Research
  • Game Theory
  • Analysis
  • Abstract Algebra
  • Number Theory
  • Cryptography
  • Graph Theory
  • Optimisation Theory
  • Functional Analysis
  • Real Analysis
  • Linear Algebra
  • Metric and Topological Spaces