Optimising IoT Networks Using 𝕷-Graph Products: A Study on Strong and Modular Products

Abstract

The graph product 𝐺 ⊙ 𝐻 defines a combination of two graphs into a new graph, with a set of vertices and edges derived from the original graphs, providing a structured representation of relationships. This paper discusses graph products using lattice graphs ( 𝔏-graphs), with a particular focus on strong and modular products. We studied 𝔏-graph products, focusing on their main features and how they can be compared with each other. We used theoretical analysis and mathematical proofs to show their structures and real- world importance. Our findings indicate that strong products support efficient communication across network levels, whereas modular products optimize shared pathways, reducing congestion and energy consumption in IoT networks. These findings improve our understanding of complicated interactions in IoT systems, leading to improved network design and performance.