Author ORCID Identifier

https://orcid.org/0000-0002-4703-3438

Date of Award

7-2-2025

Document Type

Thesis

School

School of Arts, Sciences, Humanities & Education

Programme

Ph.D.-Doctoral of Philosophy

First Advisor

Dr.V.Swaminathan

Keywords

Lie Algebra, Hypergraph, Wireless Sensor Network, Vehicular Ad hoc Network, Routing

Abstract

A hypergraph is a generalized graph characterized by edges spanning more than one vertices describing multiple relationships among them. It provides a mathematical framework for comprehending and learning about a wide range of real-world challenges. On the other side, the theory of non-associative algebras, such as Jordan, Octonions, Malcev, and Lie, has found significant impetus in recent years. These structures proved intriguing from an algebraic standpoint; they generated novel concepts and approaches that aided in solving specific classic algebraic problems, also progressing towards application.

A preeminent observation that galvanizes this thesis is that hypergraph association is still unexplored in Lie algebra and its application in real-world scenarios. In this thesis, the association of hypergraph theory with Lie algebra of upper triangular matrices is carried out, followed by an application to wireless networks. We analyzed the relationship of a graph with the Lie algebra of upper triangular matrix, which leads to the association of the hypergraph with Lie algebra of upper triangular matrix. Furthermore, as the use of Lie algebra in engineering applications has yet to be adopted, we intend to apply this theory to the problem of wireless network routing.

Wireless networks are chosen due to the explosive growth of hand-held wireless devices and technologies such as mobile phones, laptops, iPads, WiFi, IoTs, etc. The data transfer in the wireless network is a highly challenging issue because of its intermittent communication. So, this study involves designing the cluster-based routing protocol for two distinct types of networks with the variation in the theory: one has nodes with static placement and the other with increased mobility nodes.

Wireless Sensor Networks has nodes with static placement, utilize Lie hypergraph theory, while Vehicular Ad hoc Networks nodes with high mobility, use Variable Lie hypergraph theory. The proposed work clusters the network with hypergraph construction, hypergraph transversal is employed to elect the cluster heads and Lie commutators are utilized to find the path with the best relay nodes for routing. Simulation is carried out to assess the performance of the proposed protocol using the metrics of average delay, packet delivery ratio, energy consumption, network lifetime, and throughput.

In addition to addressing routing challenges, ensuring secure communication among nodes is essential for the overall robustness and reliability of a network. To achieve this, a novel 2D-Henon Sine Cosine chaotic map has been developed to generate the keys required for encryption and decryption. The study evaluates various metrics, including Lyapunov exponent analysis, trajectory analysis, NIST test suite analysis, encryption and decryption time, the randomness of key, plain and cipher text values, delay, throughput, and so on.

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