Domination Numbers and Radius in Trapezoidal Graphs

Trapezoidal graphs a significant class of intersection graphs have garnered interest due to their applicability in various real-world scenarios. Defined as intersection graphs of trapezoids between two parallel lines these graphs are useful in scheduling problems bioinformatics and network design.Understanding the relationships between different domination numbers and the radius of a graph can provide deeper insights into its structure and properties. In this context we explore three specific domination numbers: the Roman domination number the total domination number and the distance-2 domination number. These parameters offer different ways of measuring how subsets of vertices can influence or dominate the entire graph.