Research
Research Interests:
Combinatorial Matrix Theory (Graph Spectra, Matrix Completion Problems)
Finite Fields and applications in Cryptography
Publications:
Linear Algebra / Combinatorial Matrix Theory:
The nonnegative Q-matrix completion problem, J. Algebra Comb. Discrete Struct. Appl., 4(1), (2017), 61-74 (with
Kalyan Sinha).The P_0^+-matrix completion problem, Electron. J. Linear Algebra, 29 (2015) 120-143 (with Kalyan Sinha).
The positive Q-matrix completion problem, Discrete Mathematics, Algorithms & Applications, 7(4) (2015), 1550052, 19 pp. (with Kalyan Sinha) .
The Q-matrix completion problem, Electron. J. Linear Algebra, 18 (2009) 176-191 (with Luz Maria DeAlba and Leslie Hogben).
Minimal configuration unicyclic graphs, to appear in Linear and Multilinear Algebra, 57(2009) 19-27 (with M. Nath).
Unicyclic graphs with the strong reciprocal eigenvalue property, Electron. J. Linear Algebra, 17 (2008) 139-153 (with S. Barik, M. Nath and S. Pati).
The spectrum of the corona of two graphs. SIAM J. Discrete Math. 21 (2007), no. 1, 47-56 (electronic) (with S. Barik and S. Pati).
On the null-spaces of acyclic and unicyclic singular graphs, to appear in Linear Algebra Appl. 427 (2007) 42-54 (with M. Nath).
Column ranks and their preservers over nonnegative real matrices. Linear Algebra Appl. 399 (2005), 3-16. (with LeRoy B.Beasley, Seok-Zun Song and Kyung-Tae Kang).
Finite Fields & Cryptography:
Poly-Dragon: an efficient multivariate public key cryptosystem, J. Math. Cryptology, Volume 4, Number 4, (2011) 349-364 (with R.P. Singh and A. Saikia)
Little Dragon two: an efficient multivariate public key cryptosystem, International Journal of Network Security and its Applications (IJNSA), Volume 2, Number 2 (2010) (with R.P. Singh and A. Saikia).
O lder Publications:
Weak and strong fuzzy homomorphisms of groups. J. Fuzzy Math. 12 (2004), no. 2, 357--368 (with Tazid Ali).
Solvable fuzzy groups. Fuzzy Sets and Systems 106 (1999), no. 3, 463--467.
Nilpotent fuzzy groups. Fuzzy Sets and Systems 101 (1999), no. 1, 167--176 (with K.C. Gupta).
Commutator fuzzy groups. J. Fuzzy Math. 4 (1996), no. 3, 655--663 (with K.C. Gupta).
Operator domains on fuzzy groups. Inform. Sci. 84 (1995), no. 3-4, 247--259 (with K.C. Gupta).
Conormal fuzzy groups. Fuzzy Sets and Systems 56 (1993), no. 3, 317--322 (with K.C. Gupta).
My PhD Students:
Milan Nath (2007): Certain aspects of spectra of unicyclic graphs.
Rajesh Pratap Singh (2010): Permutation polynomials and their applications in cryptography.
Kalyan Sinha (2015): On completion problems for some classes of matrices.
Sabyasachi Mandal (pursuing)
For a list of my MSc & BTech Project students Click Here .
A selected list of Conferences attended:
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Joint AMS-INDIA Meeting, IISc, Bangalore, 17-20 December, 2003.
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AMS Sectional Meeting, Lincoln, Nebraska, USA, 21-23 October, 2005.
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International Congress of Mathematicians (ICM 2006), Madrid, Spain, 22-30 August, 2006.
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10th International Conference on Finite Fields and their Applications, Ghent, Belgium, 11-15 July, 2011.
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International Congress on Mathematical Education (ICME 2012), Seoul, South Korea, 8-15 July, 2012.
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38th Australasian Conference on Combinatorial Math. and Combinatorial Computing, Wellington,
New Zealand, 1-5 December, 2014.
Research Level Conference/Workshop Organized:
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Instructional Workshop and International Conference on Geometric Group Theory, IIT Guwahati,
2-21 December 2002 (Member, Organizing Committee). -
Instructional Workshop on Algebraic Graph Theory, IIT Guwahati, 9-18 December, 2004 (as Coordinator).