**Dr. Tarkeshwar Singh****Dr. Tarkeshwar Singh**(born 1-August-1969) is a Graph Theorist having research interests in Graph Labeling Problems and Spectra of Signed Graphs . He has contributed to Hypergraceful Graphs and Graph Labelings.

He was awarded the "Young Scientist" award by the Department of Science and Technology (Ministry of Science and Technology, Govt. of India) for his contributions to graph theory. He is currently working as an Assistant Professor, in the Department of Mathematics, BITS Pilani, KK Birla Goa Campus, Goa.

He is a Life member of Ramanujan Mathematical Society, Forum for Interdisciplinary Mathematics and a founder member of Academy of Discrete Mathematics and Applications.

Publications |
Academics |
Mentoring |
Memberships |

**Publications**

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 C3 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 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.

15. 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.

16. T. Singh, S.B. Rao, B.D. Acharya and Mukti Acharya, Graceful complete

17. T. Singh, Skolem and hooked Skolem graceful sigraphs, Labelings of 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.

18. 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.Discrete Structures and Applications (Eds.: B.D. Acharya, S. Arumugam, and A. Rosa), Narosa Publishing House, (2008), pp. 155-164.

19. T. Singh, Jessica Pereira and S.B. Rao, k-Hypergraceful Complete Graphs, Revised and Submitted 2013.

20. T. Singh, Nutan G. Nayak, Spectra and Energy of Sigraphs, submitted 2013.

21. T. Singh, Siddharth Gupta, Mirka Miller and P. Oudone, Some Neighborhood Magic Graphs, submitted 2013.

22. T. Singh, Jessica Pereira and B.S. Panda, Embedding of Graceful Sigraphs with Graph Theoretic Property P.

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**Academics**

1. Delivered a lecture on “Graph Labeling Problems” in National Workshop on Discrete Mathematics and its Application during March 21-24, 2005 organized by the Department of Pure Mathematics, University of Kolkata, Kolkata.

2. Acted as a Tutorial leader in CARDMATH National Group Discussion on Signed Discrete Structures and their Applications, during Nov. 15-24, 2005, organized by the Regional Institute of Education, Mysore.

3. Delivered 5 lectures on “Graceful and Skolem Graceful Signed Graphs and its Applications in Design Theory”, in Group Discussion on Labelings of Discrete Structures and Applications, during April 19-28, 2006, organized by the Department of Mathematics, Mary Matha Arts & Science College, Mananthavady, Kerala.

4. Delivered 4 lectures on “Graph Labeling Problems and its Application to Coding Theory”, in National Workshop on Graph Theory and Applications, during Oct. 9-16, 2006, organized by the Department of Mathematics, North-East Regional Institute of Science and Technology (NERIST), Nirujali, Itanagar, Arunachal Pradesh.

5. Delivered an invited talk on “Construction of graceful trees from Skolem sequences” and chaired a session in National Conference on Combinatorics and Graph Theory, during March 10-12, 2007, organized by Department of Mathematics, Saurashtra University, Rajkot, Gujarat.

6. Delivered an invited talk on “Skolem gracefulness of 2-sitars” and chaired one session in Graph Theory Day III & International Conference on Recent Developments of Combinatorics and Graph Theory, during June 10-14, 2007, at Kalasalingam University, Anand Nagar, Tamil Nadu.

7. Delivered four invited talks on Applications of Graceful and Skolem graceful Signed Graphs, in National Workshop on Uniform Hypergraphs at CR Reddy International Institute of Mathematics, Eluru, Andhra Pradesh during Jan 29- Feb 5, 2008.

8. Delivered an invited talk on Graceful Signed Graphs on C3k , in 5th International Workshop on Graph Labelings, Kalasalingam University, Krishnankoil, Tamil Nadu, during Jan. 07-10, 2009.

9. Delivered 4 invited lectures on Graceful Graphs and its Application in Instructional Workshop on Graph Theory and its Application, Institute of Mathematics and Applications, Bhuvneshwer, during Dec.17 -21, 2009.

10. Delivered 3 invited Lectures on Graceful Signed Graphs and its Applications, in National Workshop on Discrete Mathematics, Banasthali University, Rajasthan, during May 1-5, 2010.

11. Delivered 4 invited lectures on Graph Labeling Problems and its Applications in refresher course in Mathematics in “Algebraic and Number Theoretic Aspects in Graphs and Applications” at UGC Academic Staff College, University of Mysore, Mysore, during June 11-12, 2010.

12. Delivered an invited talk on Neighborhood Magic Graphs in “National Conference in Distance in Graphs” during Oct. 3-5, 2010, at Department of Mathematics, Poorna Prajna College Udupi.

13. Attended and presented a research paper entitled Graceful Signed Trees, International Conference on Recent Trends in Graph Theory and Combinatorics (ICRTGC-2010), Cochin University of Science and Technology, Cochin, during August 12-15, 2010.

14. Delivered an invited talk on Embedding Skolem Graceful Graphs in the Conference on Algorithms, Computing, Graph Theory and Combinatorics, at Vishvesvaraya Technological University Belgaum, April 18-20, 2011.

15. Delivered 3 invited talks on Graph Algorithms in National Instructional Workshop on Graph Theory and Applications at DST – Center for Interdisciplinary Mathematical Sciences (DTS-CIMS BHU), Banaras Hindu University, Varanasi, during May 23-28, 2011.

16. Delivered an invited talk on Some Embedding Problems on Graceful Signed Graphs in Seventh Annual Conference of Academy of Discrete Mathematics and Application and Graph Theory Day VII at National Institute of Technology Calicut, June 9-11, 2011.

17. Acted as resource person in ISTE Approved Short Term Training Program on Graphs and Algorithms, at Padre Conceicao College of Engineering, during July 4-9, 2011.

18. Delivered an invited talk on Application of Linear Algebra in Graph Theory in National Conference on Linear Algebra and Applications at Milagres College Udupi, during August 4-5, 2011.

19. Acted as tutorial leader in Advanced School on Graph Algorithms, Department of Mathematics, Birla Institute of Technology and Science Pilani, KK Birla Goa Campus, Goa, during July, 23-27, 2012.

20. Acted as Faculty Expert in Workshop on Mathematics Project Guidelines and Evaluation, organized by State Council for Educational Research and Training (SCERT), Govt. of Goa, Goa, on Sept.6, 2012.

21. Attended and presented a paper entitled “Additively Graceful Signed Graphs” in Twenty first International Conference of FIM on Interdisciplinary Mathematics, Statistics and Computational Techniques IMSCT 2012 – FIM XXI at the Department of Statistics, Punjab University Chandigarh, during Dec. 15-17, 2012.

22. Acted as a resource person in the panel discussion "Is research a good career option?" in Research Promotion Workshop on Introduction to Graph and Geometric Algorithms at the Department of Mathematics, Birla Institute of Technology and Science Pilani, KK Birla Goa Campus, Goa, during Jan. 17-19, 2013.

23. Delivered two lectures on Discrete Mathematical Models and its Applications in a Workshop on A tribute to S. Ramanujan and Prof. S. Chandrashekhar (Life and Work) at Department of Mathematics, T.D. P.G. College (Purvanchal University Jaunpur) Jaunpur, April 18-22, 2013.

24. Presented a paper on d-Distance Neighborhood Magic Graphs in 3rd International Conference on Discrete Mathematics (ICDM-2013) held at Karnataka University Dharwad, during June 10-14, 2013.

25. Attended a Workshop on MATHEMATICA at the Department of Mathematics, Birla Institute of Technology and Science Pilani, KK Birla Goa Campus, Goa, during July, 24-25, 2013.

**Workshops Conducted**

1. Organizer of "3rd Group Monitoring Workshop cum 6th meeting of re-constituted expert panel on FAST TRACK PROPOSALS FOR YOUNG SCIENTISTS" in Physical and Mathematical Sciences held at BITS-Pilani Goa Campus during Jan. 11-12, 2007.

2. Member of the organizing committee of the International Workshop on "Advances in Computational Partial Differential Equations" holding at BITS-Pilani K.K. Birla Goa Campus from February 7 to March 5, 2011.

3. Organizer of Instructional Workshop on Graph Theory and Applications during at BITS Pilani KK Birla Goa Campus, Goa, April 28-29, 2011.

4. Academic Coordinator of National Instructional Workshop on Graph Theory and Applications, at DST Center for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi, during May 23-29, 2011.

5. Organizer of School on Graph Algorithms during at BITS Pilani KK Birla Goa Campus, Goa, December 15-19, 2011.

6. Convener of a National level “Advanced School on Graph Algorithms” at BITS Pilani KK Birla Goa Campus, Goa, sponsored by National Board of Higher Mathematics NBHM and Department of Science Technology and Environment (DSTE) Goa, during July 23-27, 2012.

7. Local convener of Research Promotion Workshop on Introduction to Graph and Geometric Algorithms, at BITS Pilani KK Birla Goa Campus, Goa, sponsored by National Board of Higher Mathematics NBHM in collaboration with School of Technology and Computer Science, Tata Institute of Fundamental Research(TIFR) Mumbai, during Jan. 17-19, 2013.

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**Mentoring**

- Guiding 2 Ph.D. Candidates in BITS Pilani KK Birla Goa Campus.

- Guided 3 Students for M.Phil. Degree, Bharthiyar University Coimbatore.
- Guided First Degree Projects in BITS Pilani KK Birla Goa Campus:
- Computer Project: 10 students (Number Theory and Application to Graph Theory).
- Study Oriented Project: 10 students (Graph Theory, Algorithmic Graph Theory, Spectral Analysis, Integral Transforms and Networks).
- Special Project: 01 students

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**Memberships**

1. Member of Editorial Board of Journal of Indian Academy of Mathematics, during 2011-2013.

2. Member of Advisory Board of Indian Academy of Mathematics, during 2013-2015.

3. Member of editorial board of Journal of Vijnan Parishad, India.

4. Member of the Reviewer Committee in Mathematical Review of American Mathematical Society (AMS).

5. Member of the advisory body of Department of Mathematics for the academic year 2010-11 in KLS Gogte Institute of Technology, Belgaum.