Faculty

Core Research Domains:

• Graph Theory (Discrete Mathematics)

Research Focus:

PhD Awarded on “Selected Topics in Graphs and Respective Codes”

In the doctoral thesis entitled “Selected Topics in Graphs and Respective Codes”, a few concepts of two major areas of mathematics, viz. Graph theory and Coding theory, were studied, as graphs play a vital role in describing real life problems, and codes are widely used for information transmission, as each being a better counter part of the other. The study was focused mainly on graph invariants and the construction of a new class of code, the Vertex code of graphs, form the graphs considered earlier in the study.The study was extended to some binary operations on two graphs and the polynomials of the resultant graphs were estimated and their characteristics were generalized.

The combinatorial information and the algebraic properties of a graph can be easily understood from its polynomials. These polynomials are also good tools to check the capability of a graph in networking. The results were published as research papers.

A new binary nonlinear code, from a given graph , was found out, in such a way that if  has a vertex set  a code  was obtained with code words so that to each vertex  of  there exists a unique code word  of with minimum block length . Certain constraints were set so as to obtain a general nature for the code words corresponding to particular vertices. An algorithm was developed to find the existence of such code of a graph.

The reverse process of retracing a graph  has been done, from any given code , assuming it to be a code of any graph, with the help of another algorithm.  Results stating the properties of these codes were obtained.

Considering the advantages of linear codes over nonlinear, an attempt was made to construct linear codes from nonlinear codes obtained in the course of study. This particular linear code had less block length compared to linear codes from graphs already discussed in the literature, and both classes of codes have same distance. Thus, the construction followed in the study can be considered as a good tool to develop a linear code from graphs of higher order. The results of these studies were published as research papers.

Journals and Conferences:

• Sreedevi S. L., N. Suresh Babu, ‘A Vertex Code of Designed Distance and its Graph ’, International Journal of Mathematics Trends and Technology, Vol. 68, Issue 6, 149 – 155, June 2022, ISSN: 2231-5373, http://www.ijmttjournal.org .
• Suresh Babu, Sreedevi S. L., ‘Vertex Codes of Graphs’, Far East Journal of Applied Mathematics, Vol. 100, Number 3, 2018, pp 197 – 215. ISSN: 0972-0960, http://www.pphmj.com .
• Suresh Babu, G. Suresh Singh, Sreedevi S. L., ‘Graphs and Codes’, International Journal of Mathematics Trends and Technology, Vol.56, April 2018, Page No. 1-9. ISSN: 2231-5373, http://www.ijmttjournal.org .
• Suresh Singh, Sreedevi S. L., ‘Neighbourhood Polynomials Derived Through Binary operations on Graphs’, International Journal of Engineering, Science and Mathematics, Vol.7, Issue 3, March 2018, Page No. 437- 451. ISSN: 2320-0294, http://www.ijesm.co.in .
• Suresh Singh, Sreedevi S. L., ‘Cartesian product and Neighbourhood Polynomial of a Graph’, International Journal of Mathematics Trends and Technology’, Vol.49, September 2017, Page No. 33-37. ISSN: 2231-5373, http://www.ijmttjournal.org .
• Suresh Singh, Sreedevi S. L., ‘Vertex Polynomials Derived Through Various Graph Theoretical Operations’, Indian Journal of Mathematics and Mathematical Sciences, Vol.13, No.2, July- December 2017, Page No. 357-367. ISSN: 0973-3329.

Conference Presentations

• ‘Neighbourhood Polynomials Derived Through Binary operations on Graphs’, at The National Conference on Discrete and Computational Mathematics, organized by The Department of Mathematics, University of Kerala, Thiruvananthapuram, January 2018.
• ‘Binary Codes from Graph Polynomials’, at The International Conference on Science, Engineering, Technology and Management, organized by Department of Mathematics, K. E. College, Mannanam, Kottayam, March 2017.
• ‘Some Results on Graph Polynomials’, at The International Conference on Agriculture, Science, Technology, Management and Social Science, organized by FATER Academy of India in Collaboration with Carmel College of Arts Science and Commerce for Women, Goa, November 2016.
• ‘Study on some relation between Codes and Graphs’, at The National Multi-Disciplinary Annual Research Conference, organized by the IQAC and School of Physical and Mathematical Sciences, University of Kerala, Thiruvananthapuram, December 2015.

FDPs, Conferences & Workshops Attended:

More than 10 + Conferences and workshops, of which the latest are:

• 5th Annual Conference of Mathematics Teachers Association(I), Jointly organized by MTA(I) & Azim Premji University, Bangalore, 09/05/2025 to 11/05/2025
• Teachers Enrichment Workshop on Linear Algebra and Differential Equations organized by NIT Warangal , 21/04/2025 to 26/04/202