Exploring Restrained Pitchfork Domination: Theory and Application Perspectives : Restrained Pitchfork Domination and Application

This paper introduces and explores the concept of restrained pitchfork domination in graph theory, a novel hybrid of restrained domination and pitchfork domination. The study defines the parameters, provides theoretical foundations, and evaluates the restrained pitchfork domination number and its inverse for various standard graphs such as paths, cycles, wheels, and bipartite graphs. Through rigorous observations and propositions, the paper reveals structural properties and conditions under which such domination exists. Moreover, the work highlights an application of restrained pitchfork domination in managing congestion within computer networks, offering a new strategy for efficient traffic control. The findings contribute to both theoretical advancements in graph theory and practical improvements in network performance optimization.