Research

Research Project Completed as a PI:

1. Hypergraceful Graphs (Fast Track Proposals for Young Scientist)

   DST No.: SR/FTP/MS-01/2003.

   Total Amount: ₹.7,92,000/. For three years.

   This project was transferred from ISI Kolkata to BITS Pilani Goa Campus after joining the mathematics department of BITS Pilani K K Birla Goa Campus.

   Funding Agency: SERC, Department of Science and Technology, Govt. of India.

 2. Studies on Neighborhood Magic Graphs.

 SERB: SR/S4/MS: 734/11.

Total Amount: ₹.12, 69,360/-

Duration: July 01, 2013 to June 30, 2016.

Funding Agency: SERB, Department of Science and Technology, Govt. of India.

 3.  Magic and Antimagic Labeling of Graphs

(Reference No. CRG/2018/002536)

Total Amount: ₹.19, 54,832/-

Duration May 27, 2019 to May 26, 2022.

Funding Agency: Science and Engineering Research Board, Govt. of India.

Ongoing Research Project as a PI:

• Identification of Gene regulators for drought resistance using network analysis and its experimental validation (jointly with Prof. Rajesh Mehrotra, Department of Biological Sciences).

Total Amount: ₹ 20,00,000/- (Ref. No. C2/24/288).

Duration: 2 years

Funding Agency: Cross Disciplinary Research Framework BITS Pilani.

• New Frontiers in Magic and Antimagic Labelling of Graphs (Jointly with Prof. Siddharth Gupta, Department of Computer Science and Information Systems).

• Total Amount: ₹4,50,000/- (Ref. No. 02011/21/2025/NBHM/R&D-II/9821).

• Duration: 3 years

• Funding Agency: National Board for Higher Mathematics (NBHM), Dept. of Atomic Energy, Government of India.

Ongoing Research Project as a Co-PI:

• XOAI: Explainability Evaluation and Out-of-Distribution Detection

Toolkit for Artificial Intelligence Systems (jointly with Prof. Hemant Rathore, Department of Computer Science and Information Systems).

Total Amount: ₹48,25,493/- (Ref. No. SAG/4600/TCG/CARS/C-80).

Duration: 2 years

Funding Agency: Defence Research and Development Organization (DRDO).

Research Papers published in International/National Journals:

1.      T. Singh and Mukti Acharya, Skolem graceful signed graphs, Extended abstract published in Electronic Notes in Discrete Mathematics, Vol. 15 (2003), 9-10.

2.      T. Singh and Mukti Acharya, Graceful signed graphs: III. The case of signed cycles in which negative sections form a maximum matching, Graph Theory Notes of New York, Vol. XLV, (2003), 11-15, MR 2040207.

3.       T. Singh and Mukti Acharya, Graceful signed graphs, Czech. Math. Journal, Vol. 54(129)(2), (2004), 291-302, MR 2059251(2005 a:05193).

4.      T. Singh and Mukti Acharya, Graceful signed graphs: II. The case of signed cycle with connected negative section, Czech. Math. Journal, Vol. 55(130)(1), (2005), 25-40, MR 2121654.

5.      T. Singh and Mukti Acharya, Graceful signed graphs: V. Union of k copies of  the cycle of length three with one vertex in common, International Journal of Management & Systems (IJOMAS), Vol. 20(3), (2004), 246-254.

6.      T. Singh and Mukti Acharya, Construction of graceful signed graphs, Defense Science Journal, Vol.56 (5) (2006), pp. 801-808.

7.      T. Singh, S.B. Rao, B.D. Acharya, Minimum robust domination energy of graphs, AKCE International Journal of Graphs Combinatorics, Vol. 4 No. 2 (2007), pp. 139-143.

8.       T. Singh and Mukti Acharya, Two signed Stars are Skolem Graceful, in  The Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 69(2009), pp. 113-124.

9.      T. Singh, Graceful Signed Graphs on C3k, AKCE International Journal of Graphs and Combinatorics, Vol. 6 No. 1(2009), pp. 201-208.

10.  T. Singh, B.D. Acharya, Mukti Acharya and S.B. Rao, Hypergraceful complete graphs, Australasian Journal of Combinatorics, Vol. 48 (2010), pp. 5-24.

11.   T. Singh and Mukti Acharya, Skolem graceful signed graphs, Utilitas Mathematica, 82(2010), 97-109.

12.  T. Singh, Utpal Roy and Veeky Baths, Disruption of Cell wall fatty acid biosynthesis in Mycobacterium tuberculosis using graph theory, Theoretical Biology and Medical Modeling 2011, 8:5 doi:10.1186/1742-4682-8-5.

13.   T. Singh and Mukti Acharya, Embedding of Sigraphs in Graceful Sigraphs, ARS Combinatoria, 111(2013), 421-426.

14.   T. Singh, Veeky Baths and Anil Kumar, Disruption of Cell wall fatty acid biosynthesis in Mycobacterium tuberculosis using the concept of minimum robust domination energy of graph, Annual Research & Review in Biology, 4(12) (2014), 2037-2041.

15.  T. Singh, Jessica Periera and S. Arumugam, On (k,d)-Skolem graceful graphs, Electronic Notes in Discrete Mathematics, 48(2015), 81-88.

16.   T. Singh, Aloysius Godinho and S. Arumugam, On S-magic graphs, Electronic Notes in Discrete Mathematics, 48(2015), 267-273.

17.   T. Singh, Jessica Periera and S. Arumugam,  A new measure for gracefulness of graphs, Electronic Notes in Discrete Mathematics, 48(2015), 275-280.

18.  T. Singh, Jessica Periera and S. Arumugam,  On (k,d)-hooked Skolem graceful graphs,  Journal of Combinatorics, Information & System Science, 41 No.1-3(2016), 7-15.

19.  T. Singh, Veeky Baths, S. Indumathi and S. Arumugam, Graph theoretic concepts in the study of biological networks,  Applied Analysis with Applications in Biological and Physical Sciences (2016), 187-200.

20.   T. Singh, Veeky Baths, Marina Dhara and S. Arumugam,  Analysis of Tuberculosis-Human Protein Interaction Network using Centrality Measure(accepted 2016).

21.  T. Singh, A.K. Handa, Aloysius Godinho and S. Arumugam, Distance Antimagic Labeling of Join and Corona of two Graphs, AKCE International Journal of Graph and Combinatorics, 14(2017), 172-177.

22.  T. Singh and Aloysius Godinho, Some Distance Magic Graphs, Electronic Notes in Discrete Mathematics, 63(2017), 311-315.

23.  T. Singh, A.K. Handa and Aloysius Godinho, Distance Antimagic Labeling of Ladder Graphs, Electronic Notes in Discrete Mathematics, 63(2017), 317-322.

24.  T. Singh and Aloysius Godinho, Some Distance Magic Graphs, AKCE International Journal of Graph and Combinatorics, 15(1) (2018), 1-6.

25.  T. Singh, Aloysius Godinho and S. Arumugam, The Distance Magic Index of a Graph, Discussiones Mathematicae Graph Theory, 38(1)(2018), 135-142.

26.  T. Singh,  Manoj Kumar Singh, Dharm Raj Singh and Rajkishore Prasad,  Genetic Algorithm for Solving Multiple Travelling Salesmen Problem using a new Crossover and Population Generation, Computación y Sistemas, Vol. 22, No. 2 (2018), 491–503.

27.  T. Singh, S.B. Rao, E. Sampathkumar, Mukti Acharya and B.D. Acharya, Saturated Edge Coverings of Graphs,  Indian Journal  of Discrete Mathematics, Vol. 4(1) 2018, Published in 2019. ISSN: (2455-5819).

28.  T. Singh, Jessica Pereira and S. Arumugam, Edge Consecutive Graceful Labeling of a Graph, Discrete Applied Mathematics, 280(2020), 214-220.

29.  T. Singh, Jessica Pereira and S. Arumugam, k-Hypergraceful Complete Graphs, Indian Journal of Discrete Mathematics, Vol.7(2)(2021), 133-145.

30.  T. Singh, Jessica Pereira and S. Arumugam, Additively Graceful Signed Graphs, AKCE International Journal of Graph and Combinatorics, Vol . 20(3) (2023), 300-307.

31.  T. Singh, Teja Sai Ram, Sawlani Shivam, V. Lokeshwar Reddy, V.P. Agarwal, Anasuya Ganguly, Graph Theoretical Model and Analysis of Carbon Cycle, International Journal of Chemical and Environmental Sciences, Vol.4(2)(2023), 7-23.

32.  T. Singh, Aloysius Godinho, A.K. Handa, On Local Distance Antimagic Labeling of Graphs, AKCE International Journal of Graph and Combinatorics  Vol. 21(1)(2024), 91-96. Accepted 04 Sep 2023, Published online: 30 Oct 2023.

33.  T. Singh and Ravindra K. Pawar, Distance Magic Labeling of Mycielskian Graphs, Electronic Journal of Graph Theory and Applications, Vol. 12(1) (2024), 75-88.

34.  T. Singh, Ravindra K. Pawar and J.S. Bagga, Super Total Local Antimgaic Vertex (Edge) Coloring of Graphs, Bulletin of the Institute of Combinatorics and its Applications,  103 (2025), 82–113.

35.  T. Singh, Jessica Pereira and S. Arumugam, Embedding of Graceful Sigraphs with Graph Theoretic Property P, Indian Journal of Discrete Mathematics, Vol. 10(1) (2024), 13-25.

36.  Ravindra Pawar, T. Singh, Adarsh Kumar Handa and Aloysius Godinho, Local Antimagic Coloring of some Graphs, South East Asian J. of Mathematics and Mathematical Sciences, Vol. 20(2) (2024), 01-14.

37.  T. Singh, Ravindra K. Pawar, Himadri Mukherji and J.S. Bagga, A Complete Characterization of Magic Constants Arising from Distance Magic Graphs Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 123(2024), 287-302.

38.  T. Singh and Ravindra K. Pawar, Distance Magic Labeling of Generalized Mycielskian Graphs, Proceeding of Jangjeon Mathematical Society (PJMS), Vol. 29(2)(2026), 269-286.

39.  T. Singh and Maurice Almeida, D-distance Magic Labelling of Circulant Graphs (2025), accepted Communications in Combinatorial Optimization.

40.  T. Singh and Maurice Almeida, Some Results on Local Distance Antimagic Chromatic Number of Graphs (2026), accepted Communications in Combinatorial Optimization. 

  Research Papers published in Proceedings:

1.      T. Singh and Mukti Acharya, Characterization of signed graphs whose negations are switching equivalent to their iterated line sigraphs, Proc. of Conference of Graph Theory and Applications (CGTA-2001) (Eds.: R.J. Wilson, R. Balakrishnan and G. Sethuraman), Narosa Publishing House Pvt. Ltd. (2004), 15-24.

2.      S.B. Rao, T. Singh and V. Parameswaran, Some sigma labeled graphs: I. Proc. of National Conference of Graphs, Combinatorics, Algorithms and Applications (NCGCAA-2004) (Eds.: S. Arumugam, B.D. Acharya and S.B. Rao), Narosa Publishing House Pvt. Ltd. (2004), 125-134.

3.      T. Singh, S.B. Rao, B.D. Acharya and Mukti Acharya, Graceful complete signed graphs, Extended abstract published in Proc. of National Conference of Graphs, Combinatorics, Algorithms and Applications (NCGCAA-2004) (Eds.: S. Arumugam, B.D. Acharya and S.B. Rao), Narosa Publishing House Pvt. Ltd. (2004), 123-124.

4.      T. Singh,  Skolem and hooked Skolem graceful sigraphs, Labelings of Discrete Structures and Applications (Eds.: B.D. Acharya, S. Arumugam, and A. Rosa), Narosa Publishing House, (2008), pp. 155-164.

5.      Tarkeshwar Singh, Manoj Kumar Singh and Dharm Raj Singh, A hybrid heuristic algorithm for Euclidean traveling salesman problem, IEEE Proc. International Conference on Computing, Communication and Automation(ICCCA 2015) (2015),  767-772.

6.  Tarkeshwar Singh, Manoj Kumar Singh and Dharm Raj Singh, A Hybrid Algorithm with Modified Inver-Over Operator and Genetic Algorithm Search for Traveling Salesman Problem, Advanced Computing and Communication Technologies, Springer Singapore (2016), 141-150.

7.      Adarsh K. Handa, Aloysius Godinho, and T. Singh, Some Distance Antimagic Labeled Graphs, Proc. Algorithms and Discrete Applied Mathematics (CALDAM 2016) (Eds. Satish Govindrajan and Anil K. Maheshwari), Lecture Notes in Computer Science (LNCS) Vol. 1906 (2016), 190-200.

8.      T. Singh, Jessica Periera and S. Arumugam, m-Gracefulness of Graphs, Proc. Algorithms and Discrete Applied Mathematics (CALDAM 2016)(Eds. Satish Govindrajan and Anil K. Maheshwari), Lecture Notes in Computer Science (LNCS) Vol. 1906 (2016), 289-298.

9.      T. Singh and Aloysius Godinho,  Group Distance Magic Labeling of Cnr Proc. Algorithms and Discrete Applied Mathematics (CALDAM 2016)(Eds. Daya Gaur and N.S. Narayanaswamy), Lecture Notes in Computer Science (LNCS) Vol. 10156 (2017), 187-192.

10.    T. Singh and Aloysius Godinho and S. Arumugam,  Nearly Distance Magic Graphs Proc. International Conference on Theoretical Computer Science and Discrete Mathematics (ICTCSDM 2016) (Eds. S. Arumugam, Jay Bagga, Lowell W. Beineke and B.S. Panda), Lecture Notes in Computer Science (LNCS) Vol. 10398 (2017), 76-82, DOI: 10.1007/978-3-319-64419-610.