Author ORCID Identifier
0000-0002-9622-1283
Biosketch
S. Shanmugavelan is a Mathematics Educator, Researcher, and Assistant Professor with nearly a decade of teaching experience across Engineering, Science, Arts, and Management education. He holds a five-year Integrated M.Sc. with B.Ed. in Mathematics from the Srinivasa Ramanujan Centre (SRC), SASTRA Deemed University, Kumbakonam, where he graduated as the School of Education Topper. He subsequently obtained an M.Phil. in Mathematics from A.V.V.M. Sri Pushpam College, Thanjavur, affiliated to Bharathidasan University.
He began his academic career as an Assistant Professor at K. Ramakrishnan College of Engineering, Trichy and later joined his alma mater, the Srinivasa Ramanujan Centre (SRC), SASTRA Deemed University. He was awarded his Ph.D. in Graph Theory in 2026 by SASTRA Deemed University, Thanjavur, for his research on distance-based domination in graphs and their applications.
His research interests include domination theory,interconnection networks, number-theoretic graphs, topological indices, QSPR, and computational applications. His technical expertise includes Python, MATLAB, R, and LaTeX.
A student-friendly and innovative educator, Dr. Shanmugavelan has developed handwritten teaching materials for more than 20 courses. His professional journey is guided by the principles of Teaching, Research, and Continuous Learning, with a strong commitment to inspiring curiosity, fostering independent thinking, and promoting meaningful learning.
Date of Award
19-9-2026
Document Type
Thesis
School
School of Arts, Sciences, Humanities & Education
Programme
Ph.D.-Doctoral of Philosophy
First Advisor
Dr.C.Natarajan
Keywords
Graph Theory, Domination Theory, Interconnection Networks, Domination-Based Energies, QSPR Analysis
Abstract
Distance-based domination has emerged as a significant development in graph theory, attributed to its applications in communication systems, interconnection networks, parallel architectures, and chemical graph models. This thesis focuses on two such graph invariants: hop domination number and 2-hop domination number of graphs. The hop domination number of some generalized graph structures like generalized thorn paths, generalized theta graphs, and snake graph families is studied along with a newly introduced family, namely generalized ciliates.
Moreover, a variant of hop domination number, namely, the 2-hop domination number, is studied for some grid families like ladder, hexagonal grid, and its variants. Furthermore, a characterization for all trees attaining the equality of 2-hop domination number and total domination number is explored. In addition to the theoretical developments on graph families, this work extends the study of distance-based domination to important classes of interconnection networks, including octagonal networks, honeycomb mesh networks, and butterfly networks.
These network architectures are widely recognized for their relevance in large-scale communication systems and parallel processing environments. This thesis establishes some upper and lower bounds of hop and 2-hop domination numbers of these networks. Furthermore, a comprehensive Quantitative Structure-Property Relationship (QSPR) investigation is conducted using distance-based domination energy descriptors, including Hop Domination Energy (HDE) and its associated variants. In this framework, the newly introduced 2-Hop Domination Energy (2HDE) and its corresponding extensions are systematically incorporated as molecular descriptors.
Their predictive capabilities are examined in relation to selected physico-chemical properties of benzenoid hydrocarbons (BHCs), thereby assessing the effectiveness of domination-based energy descriptors. Further, an algorithm is developed for computing these descriptors along with classical domination-based energy descriptors like domination energy, total and connected domination energies. Moreover, the Estrada and Resolvent versions of these domination-based energy descriptors are also introduced, and their numerical values are computed for 35 BHCs.
With the help of these computed values, a QSPR analysis is performed using these 15 domination-based energy descriptors and some of the physico-chemical properties of BHCs. Thus, this study establishes a relationship between domination theory and chemical graph theory. To enhance the stability and reliability of the predictive performance of the model, k-fold cross-validation and external validation for a few unseen data are employed, along with a model comparison criterion to some classical topological indices, and predictive capabilities of these model’s performance are captured.
Recommended Citation
S, Shanmugavelan Mr, "A Study on some Distance based Domination Parameters in Graphs and their Applications" (2026). Theses and Dissertations. 226.
https://knowledgeconnect.sastra.edu/theses/226