cultivating efficiency: streamlining food delivery logistics through graphical networks and eternal m-certified domination number

The increasing demand for food delivery services driven by technological innovations has led to a surge in online shopping and food ordering. efficient logistics play a crucial role in connecting customers with restaurants seamlessly. in this context, the practical application of graphical networks is explored in this article to streamline food delivery operations. we introduce a novel parameter eternal m-certified domination number denoted by γmcer∞(g) , which represents the minimum number of guards needed to handle any sequence of single orders using multiple-guard movements, ensures that the guard arrangement consistently constitutes a certified dominating set. a case study is presented, illustrating how this concept can be employed to de-crease human resources in a food delivery start-up. this research contributes to optimizing food delivery logistics and reducing operational costs, thereby enhancing the efficiency of the food delivery industry.