Summary of the Event
Day 1
Date & Time
06.05.2026, 02.00 PM IST
Topic: Spectral Graph Theory
Resourse Person Dr. Rajesh Kannan Associate Professor
Faculty of Arts and Science Department of Mathematics Indian Institute of Technology, Hyderabad, India
The program began with the Tamizhthaai Vaazhthu, followed by the virtual lighting of the lamp. The Head of the Department, Department of Mathematics, SRMIST Ramapuram, gave a brief introduction and welcomed the participants. Dr. M. Nithya delivered the introduction to the speaker.
Prof. Rajesh Kannan conducted the session by introducing fundamental concepts of graph theory with simple examples. He explained important graph matrices such as adjacency, Lapla-cian, and normalized Laplacian, along with their construction and properties. He also highlighted the connection between spectral graph theory and linear algebra, particularly eigenvalues.
Further, he discussed graph isomorphism and its relation to permutations, along with key concepts such as chromatic number, Cayley’s formula, and spanning trees. The session concluded with insights into the limitations and effectiveness of spectral methods in graph analysis, along with a discussion of open problems in the field.
Day 2
Date & Time
07.05.2026, 02.00 PM IST
Topic: Realizable Properties of Graphs
Resourse Person Ismail Naci Cangul Professor
Faculty of Arts and Science Department of Mathematics Bursa Uludag University, Turkey
Prof. Ismail Naci Cangul started the session by introducing the concept of realizable graphs with simple examples. He also explained Fermat’s Last Theorem, Goldbach’s Conjecture, and discussed combinatorial problems related to graphs.
He gave a detailed explanation of the degree sequence of graphs and introduced the Omega invariant of a graph along with its formula. He also highlighted the relationship between the Omega invariant, vertices, and edges of a graph.
Further, he discussed the cyclomatic number of connected realization graphs with maximum and minimum numbers of components in a detailed manner. He also explained algebraic graphs dealing with idempotent total graphs for commutative rings with identity.
The session concluded with insights into the limitations and effectiveness of realizations of graphs with components in graph theory, along with a discussion on open problems in the field. The session concluded with the vote of thanks by Dr. R. Binthiya.
Day 3
Date & Time
08.05.2026, 02.00 PM IST
Topic: Adjacency Matrices of Graphs and their Applications
Resourse Person Prof. A. V. Chitra Professor
Department of Mathematics National Institute of Technology Calicut, India
Prof. A. V. Chitra delivered an insightful lecture on adjacency matrices of graphs and their applications. She began the session with the basic theorems of graph theory and explained the construction of adjacency matrices for several families of graphs with suitable examples. She further discussed important theorems related to adjacency matrices, particularly focusing on the number of walks and the number of triangles present in a graph.
The speaker also introduced the concept of spectral norm of symmetric matrices and elaborated on advanced topics such as Kronecker product, Cartesian product graphs, and strong product graphs. In addition, she explained cospectral graphs and isometric graphs with cospectral prop-erties, highlighting their significance in spectral graph theory.
Further, the session covered the concept of graph energy and equienergetic graphs, along with their mathematical properties and applications. The lecture provided participants with a deeper understanding of the relationship between graph structures and matrix theory. The session con-cluded with the vote of thanks by Dr. B. Roopa.
Day 4
Date & Time
09.05.2026, 02.00 PM IST
Topic: Applications of Graph Theory in Machine Learning
Resourse Person Prof. Slamin Professor
Vice Rector of Academic Affairs University of Jember
Indonesia
Prof. Slamin delivered an informative session on the applications of graph theory in machine learning. He explained the relationship between data science, artificial intelligence, and machine learning, and highlighted the role of mathematics in machine learning.
He also discussed graph representations and their applications in areas such as social networks, computer networks, disease pathways, and food webs. The session covered node-level, link-level, and graph-level machine learning tasks with examples. Further, he explained graph machine learning, its types, modern ML tools, and the differences between graph ML and conventional machine learning. The session provided valuable insights into the applications of graph theory in modern machine learning. The session concluded with the vote of thanks by Dr. J. Bala Samuel.
Day 5
Date & Time
11.05.2026, 02.00 PM IST
Topic: Colouring of graphs
Resourse Person Dr. T. Kavaskar Assistant Professor
Department of Mathematics Central University of Tamil Nadu Thiruvarur, Tamil Nadu, India
Dr. T. Kavaskar conducted the session by introducing concepts related to graph colouring with interpolation theorem and simple examples. He explained proper colouring, k-colouring, and chromatic number of graphs in detail.
He also discussed Petersen graphs and introduced Grundy colouring of graphs along with its al-gorithm. Further, he highlighted the relationship between chromatic number and greedy number of a graph. The session also covered perfect graphs, maximum and minimum degree, and the largest complete graph. In addition, he explained Brooks’ theorem and interpolation theorem related to the maximum degree of graphs.
The session concluded with discussions on chromatic number, achromatic number, and open problems in partial Grundy colouring. The session concluded with the vote of thanks by Mr. S. Perumal.
Day 5
Date & Time
12.05.2026, 02.00 PM IST
Topic: Fuzzy Graph and its Applications in Decision Making Problems
Resourse Person Dr. Deva Nithyanandham Post Doctoral Research Fellow
Research Centre of Applied Mathematics Shenzhen MSU-BIT University Shenzhen, China
Dr. Deva Nithyanandham delivered an informative session on fuzzy graphs and their applica-tions in decision-making problems. He started the session with the fundamental concepts of graph theory and explained connected graphs, competition graphs, fuzzy sets, and crisp sets. The session further covered fuzzy relations, bipolar fuzzy graphs, and bipolar fuzzy digraphs along with their components and characterizations. He also introduced a decision-making model with an algorithm and highlighted the role of bipolar fuzzy concepts in solving decision-making problems in graphs. In addition, he discussed P-competition graphs with numerical illustrations. The session concluded with applications of fuzzy graphs in COVID-19 vaccination analysis in-volving Covishield and Covaxin using algorithms and preference relations. The vote of thanks was delivered by Mrs. R. Senthamizhselvi.
Day 5
Date & Time
14.05.2026, 10.00 AM IST
Topic: Algebraic Properties for Eulerian Trials
Resourse Person Dr. Meenakshi Paramasivan Post Doctoral Fellow
Department of Mathematics and Computer Science Leipzig University, Germany.
Dr. Meenakshi Paramasivan delivered an insightful lecture on automata and its connection with graph theory. The session began with the meaning of words in automata and explained how words can be connected with graphs using automata concepts. The speaker also discussed Eu-lerian trails with reference to the famous Ko¨nigsberg bridge problem and introduced Eulerian words with suitable examples.
Further, the lecture focused on algebraic properties such as graph representation and word rep-resentation. The speaker also explained hole-free Eulerian words and discussed the related al-gorithm in detail. The session provided valuable insights into the applications of automata in graph theory and combinatorics.
Following the resource talk, the valedictory session was conducted and was gracefully hosted by Dr. J. Saral. The FDP report was presented by Dr. S. Dhanalakshmi, highlighting the activities and outcomes of the seven-day program. Participants also shared their valuable feedback and expressed their appreciation for the informative sessions conducted during the FDP.
The program concluded with a vote of thanks delivered by Dr. N. Sujatha. The session ended with the National Anthem, followed by a photo session.
More than 250 participants attended the FDP programme actively participated in the discus-sions.
