Resolving Domination Number of Graphs Derived from Certain Structures

Abstract

This research focuses on the investigation of resolving dominating sets, which possess both resolving and dominating properties. The domination number and metric dimension are terms used to describe the least order of dominating and resolving sets, respectively, and have garnered significant attention from researchers worldwide in the past decade. The primary aim of this project is to explore the application of Triglyceride structures in the analysis of resolving dominating sets. Triglycerides are formed by combining glycerol and three fatty acid groups and constitute a major component of natural fats and oils. By com- prehending the role of triglycerides in the body and actively maintaining their equilibrium, individuals can enhance their overall health and minimize associated complications. This study specifically aims to examine the resolving domination number of specific graphs de- rived from triglycerides, including the line graph and paraline graphs associated with the aforementioned structure.