Prof. Dr. Sarfraz Ahmad
Professor, Mathematics
Area of Interest: Algebraic Statistics, Combinatorics, Commutative Algebra
Tel # (Off): 111-001-007   (167)
HEC approved PhD Supervisor

Field of Specialization (Mathematics)

  • Combinatorial Commutative Algebra (Ph. D)
  • Combinatorics (Post Doctorate)
  • Graph Theory (Research Visits)

International Research Collaborations

  • Department of Mathematics and Computer Science, Phillips Universität Marburg, Germany.             (November 2011 – till date)

International Research Visits

As Visiting Scientist:

  • United Arab Emirates University, U. A. E.(August, 2017 – May, 2018)
  • Philipps-Universität Marburg, Germany(November – December, 2016)
  • Philipps-Universität Marburg, Germany(August – September, 2015)
  • Abdus Salam International Center of Theoretical Physics, Trieste, Italy (July – August, 2010)


·         U. S. A.

·         U. A. E

·         U. K.

·         Hong Kong

·         Switzerland

·         France

·         Thailand

·         Laos

·         Australia

·         Germany

·         Brazil


·         Italy

·         Romania

·         South Korea

·         Spain

·         Saudi Arabia


Reseach Students Supervised

  • Ph.D Level
  • Arfan Ali 
  • Muhammad Nadeem 
  • Nighat Farah (in progress)
  • MS Level
  • Shahid Muhmood (Poset's Partitions and Stanley Decomposition)
  • Muhammad Shafique (On the Stanley Reisner ideal of the subdivision of a simplicial complex)
  • Nazakat (On the Transformation Matrices of the subdivision of a simplicial complex)
  • Farrukh Ejaz (On the Path Ideals of the Hararay Graph)
  • Narjis Ikhlaq (On the Alexander Dual of the Cycle Graph the Path Ideals)
  • Nighat Farah (On Some Polynomials of the Chemical Nanotubes)
  • Fareeha Amber (On Automorphism Group Action and Topological Indices)
  • Farah Iqbal (On Some Topological Indices and Algebraic Properties of the Polymino Chains of 4k Cycles)
  • Khursheed Qamar (On some algebraic properties of the ideals associated to the finite posets)
  • Tahira Majeed (On different classes of Monomial Ideal associated to Lcm-lattices)
  • Iqra Siddique (On Tchebyshev Subdivisions of Simplicial Complexes) 
  • Hafiza Arham Maqbool (On algebraic properties of cover relations) 
  • Iqra Farman (Randic, Seidel and Laplacian Energy of NEPS of Cyclic Graphs)
  • Rauf Irshad (On Chromatic Subdivision of simplicial Complexes) 
  • Yasir Ali (Randic , Seidel and Laplacian Energy of NEPS Graph) 
  • Husna Muzzafar ( On Algebraic and Combinatorial Properties of the Poset C2 xC2 x Cj) 
  • Muhammad Awais (Optical Soliton Solutions for Nonlinear Schrodinger Equations with Various) 
  • Ezza Ghafoor (On Metric Dimension of Block Shift Network) 
  • Mahwish Butt (Total Edge Irregularity Strength of Interconnection Network) 
  • Saima Sami Khan (Computing the Edge Irregularity Strength for Categorical Product of
  • Some Graphs) 
  • Saman Javed (Total Edge Irregularity Strength of Triangulate Networks) 

Ongoing Research Projects:

Graduate Research Assistantships in Developing Countries (GRAID)

  • Role: National Principal Investigator
  • Awarding Body: IMU, Germany
  • Duration: July 2019 – June 2026
  • Amount: Pak Rupees 12 millions

Completed Research Projects:

National Research Grant Program (Research Project)

  • Title: Properties of Ranking Ideals
  • Role: Principal Investigator
  • Awarding Body: Higher Education Commission of Pakistan
  • Duration: July 2016 – June 2018
  • Amount: Pak Rupees 1 million

National Research Grant Program (Research Project)

  • Title: Algebraic and Combinatorial Aspects of Subdivided Complexes
  • Role: Principal Investigator
  • Awarding Body: Higher Education Commission of Pakistan
  • Duration: July 2017 – June 2019
  • Amount: Pak Rupees 1.3 millions


1. Sarfraz Ahmad (2009), "Sequentially Cohen-Macaulay and Regularity of Monomial Ideals", published by: Lambert Academic Publishing, Standard: 978-3-8383-3999-3   
Journal Papers:
1. H. Yang, M. A. Rashid, S. Ahmad, M. K. Siddiqui, M. F. Hanif (2019), "Cycle super magic labeling of pumpkin, octagonal and hexagonal graphs", Journal of Discrete Mathematical Sciences & Cryptography, pp: 1165-1176, Vol: 22, Issue: 7   
2. M. Imran, M. K. Siddiqui, S. Ahmad, M. F. Hanif, M. H. Muhammad & M.R. Farahani (2019), "Topological properties of benzenoid, phenylenes and nanostar dendrimers", Journal of Discrete Mathematical Sciences & Cryptography, pp: 1229–1248, Vol: 22, Issue: 7   
3. M. Imran, S. S. Khan, S. Ahmad, M.F. Nadeem, M. K. Siddiqui (2019), "New results on super edge magic deficiency of kite graphs", ", International Journal of Applied Mathematics, pp: 969-980, Vol: 32, Issue: 6   
4. H. Yang, M.A. Rashid, S. Ahmad, S. S. Khan, M. K. Siddiqui (2019), "On Molecular Descriptors of Face-Centred Cubic Lattice", Processes, pp: 1-15, Vol: 7   
5. H. Yang, M. H. Muhammad, M.A. Rashid, S. Ahmad, M. K. Siddiqui, M. Naeem (2019), "Topological Characterization of the Crystallographic Structure of Titanium Difluoride and Copper (I) Oxide", Atoms, pp: 1-10, Vol: 7   
6. M. Nadeem, S. Ahmad, M. K. Siddiqui, M. Naeem (2019), "Topological Descriptor of 2-Dimensional Silicon Carbons and Their Applications", Open Chemistry, pp: 1473-1482, Vol: 17   
7. M. Rafiullah, H. A. Siddiqui, Sarfraz Ahmad (2019), "Resolvability of some convex polytopes", Utilitas Mathematica, pp: 309-328, Vol: 111   
8. Hai-Xia Li, Sarfaraz Ahmad, and Iftikhar Ahmad (2019), "Topology-Based Analysis of OTIS (Swapped) Networks OKn and OPn", Journal of Chemistry , pp: 1-11, Vol: 2019, Issue: 1   
9. M. Imran, M. Arfan Ali, S. Ahmad, M. K. Siddiqui, A. Q. Baig (2018), "Topological Characterization of the Symmetrical Structure of Bismuth Tri-Iodide", Symmetry, pp: 1-15, Vol: 10   
10. H. Yang, M. K. Siddiqui, M. Ibrahim, S. Ahmad, A. Ahmad (2018), "Computing the Irregularity Strength of Planar Graphs", Mathematics, pp: 1-12, Vol: 6   
11. Juan L.G. Guirao, S. Ahmad, M. K. Siddiqui, M. Ibrahim (2018), "Edge Irregular Reflexive Labeling for Disjoint Union of Generalized Petersen Graph", Mathematics, pp: 1-10, Vol: 6   
12. Nadeem Azhar, Abdul Jawad, Sarfraz Ahmad, Iftikhar Ahmed (2018), "Cosmological Implications of Dark Energy Models in Modified Gravity", International Journal of Geometric Methods in Modern Physics , pp: 1-14, Vol: 15, Issue: 1, Standard: 0219-8878, Impact Factor: 1.068    (External URL)
13. Sarfraz Ahmad, Volkmar Welker (2018), "On Partial Barycentric Subdivision", Results Math , Vol: Online first, Standard: 1422-6383, Impact Factor: 0.693    (External URL)
14. Tahir Rizvi, Kashif Ali, Sarfraz Ahmad, Shamoon Bashir, Muhammad Younis (2017), "Bell and kink type soliton solutions in birefringent nano-fibers", Optik, pp: 327–333, Vol: 142, Issue: 1, Standard: 0030-4026, Impact Factor: 0.742    (External URL)
15. Uzma Ahmad, Sarfraz Ahmad, Rabia Yousaf (2017), "Computation of Zagreb and Atom bond connectivity Indices of Certain Families of Dendrimers by using Automorphism Group Action", Journal of the Serbian Chemical Society, pp: 151-162, Vol: 82, Issue: 2, Standard: 0352-5139, Impact Factor: 0.997    (External URL)
16. S. T. R. Rizvi, S. Bashir, K. Ali, S. Ahmad (2017), "Jacobian elliptic periodic traveling wave solutions for Biswas–Milovic equation", Optik, pp: 582–587, Vol: 131, Issue: 1, Standard: 0030-4026, Impact Factor: 0.742    (External URL)
17. Abdul Jawad, Amara Ilyas, Sarfraz Ahmad (2017), "Shaft Potential Inspired Warm Inflation", International Journal of Geometric Methods in Modern Physics, pp: 1-14, Vol: 14, Issue: 6, Standard: 0219-8878, Impact Factor: 1.068    (External URL)
18. Sarfraz Ahmad, Volkmar Welker (2016), "Chain Blockers and Convoluted Catalan Numbers", Order, pp: 347-358 , Vol: 33, Issue: 2, Standard: 0167-8094, Impact Factor: 0.621    (External URL)
19. Jia-Bao Liu, Sarfraz Ahmad, Uzma Ahmad, Mohammad Reza Farahani, Muhammad Imran, Nighat Farah (2016), "On certain topological indices of TUC5C8 nanotubes", Journal of Computational and Theoretical Nanoscience, pp: 9158-9161, Vol: 13, Issue: 1, Standard: 1546-1955, Impact Factor: 1.34    (External URL)
20. Li Yan, Yingfang Li, Sakander Hayat, Muhammad Imran, Hafiz Muhammad Afzal Siddiqui, Sarfraz Ahmad and Mohammad Reza Farahani (2016), "On degree-based and frustration related topological indices of single-walled titania nanotubes", Journal of Computational and Theoretical Nanoscience , pp: 9027-9032, Vol: 13, Issue: 1, Standard: 1546-1955, Impact Factor: 1.34    (External URL)
21. Sarfraz Ahmad (2016), "On the Chain Blockers of a Poset", MATH. REPORTS , pp: 205-215, Vol: 18, Issue: 68, Standard: 2285-3898, Impact Factor: 0.118    (External URL)
22. Sarfraz Ahmad, Uzma Ahmad, Muhammad Imran, Nighat Farah (2016), "The Omega and Sadhana polynomials of TUC4[p,q] nanotubes", Canadian Journal of Chemistry , pp: 490 – 493, Vol: 94, Issue: 5, Standard: 0008-4042, Impact Factor: 1.061    (External URL)
23. Sarfraz Ahmad, Imran Anwar (2015), "On Characteristic Poset and Stanley Decomposition of S/I", Algebra Colloquium, pp: 739–744, Vol: 22, Issue: Spec 1, Standard: 1005-3867, Impact Factor: 0.298    (External URL)
24. Sarfraz Ahmad (2015), "On the evaluation of a subdivision of the ladder graph", The Punjab University Journal of Mathematics, pp: 15-19, Vol: 47, Issue: 1, Standard: 1016-2526, Impact Factor: 0    (External URL)
25. Sarfraz Ahmad, Imran Anwar, Ayesha Asloob Qureshi (2014), "On Characteristic Poset and Stanley Decomposition", Analele Stiintifice ale Universitatii Ovidius , pp: 21-28, Vol: 22, Issue: 2, Standard: 1224-1784, Impact Factor: 0.333    (External URL)
26. Sarfraz Ahmad, Imran Anwar, Azeem Haider, Amina Inam (2013), "Inclusion Ideals Associated to Uniformly Increasing Hypergraphs", Studia Sci. Math. Hungarica, pp: 199-206, Vol: 50, Issue: 2, Standard: 0081-6906, Impact Factor: 0.621    (External URL)
27. Sarfraz Ahmad, Kashif Ali, Imran Anwar, Muhammad Hussain (2013), "Magic labeling of type (a,b,c) of subdivided ladders", Submitted for Publication   
28. Sarfraz Ahmad, Imran Anwar (2013), "On Characteristic Poset and Stanley Decomposition", Algebra Colloquium, Impact Factor: 0.237   
29. Sarfraz Ahmad (2013), "On f and h triangle of a Simplicial Complex", Czechoslovak Mathematical Journal , pp: 989-994, Vol: 63, Issue: 4, Standard: 0011-4642, Impact Factor: 0.288    (External URL)
30. G. Abbasi, Sarfraz Ahmad, Imran Anwar, W. Baig (2012), "f-ideals of degree 2", Algebra Colloquium, pp: 921-926, Vol: 19, Issue: 2012   
31. Sarfraz Ahmad, Volkmar Welker (2012), "On Partial Barycentric Subdivision", Preprints 2012   
32. Sarfraz Ahmad (2011), "Stanley decompositions and polarization", Czechoslovak Mathematical Journal, pp: 483-493, Vol: 61, Issue: 2, Impact Factor: 0.262   
33. Sarfraz Ahmad, Imran Anwar (2008), "Upper Bound for the regularity of ideals of Borel type", Communications in Algebra, pp: 670-673, Vol: 36, Issue: 2008, Impact Factor: 0.347   
34. Sarfraz Ahmad, Dorin Popescu (2007), "Sequentially Cohen-Macaulay Monomial Ideals of Embedding Dimension Four", Bull. Math. Soc. Sci. Math. Roumanie, pp: 99-110, Vol: 2, Issue: 50(98), Impact Factor: 0.507   
35. Sarfraz Ahmad, Angle Popescu (2006), "The action of automorphism group on discrete rank 1 Valuation of K[X]", Journal of Prime Research in Mathematics , pp: 198-202, Vol: 2, Issue: 2006   
Conference Papers:
1. Sarfraz Ahmad, Imran Anwar (2009) "Stable Ideal and Stanley Conjecture", Proceedings 4th World Conference on 21st Century Math.    


Post Doctorate Combinatorics & Commutative Algebra
Philipps-Universität Marburg, Germany.
2010 to 2011
Ph. D Mathematics
Abdus Salam School of Mathematical Sciences, Pakistan.
2004 to 2008
M. Sc. Mathematics
University of the Punjab, Lahore., Pakistan.
1999 to 2001


Associate Professor
COMSATS University Islamabad, Lahore Campus
Jul 2014 to Date
Assistant Professor
COMSATS Institute of Information Technology, Lahore, Pakistan.
Jan 2008 to Jun 2014
Visiting Researcher
Abdus Salam ICTP, Trieste, Italy.
Jul 2010 to Aug 2010
Visiting Lecturer
Punjab University College of Information Technology, Punjab University
Jan 2003 to Jun 2004
Virtual University of Pakistan
Apr 2001 to Aug 2004

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