Advanced Mathematical Models & Applications

In graph theory, domination is an important concept with many practical applications. Different types of domination have been defined based on the structure of dominating sets. In this study, we propose a new domination parameter by focusing on the edges of a graph, inspired by the concept of Modern Roman domination, which models defense strategies. This new concept, called the Edge Modern Roman domination, assigns labels to the edges of a graph in such a way that each edge without defense is supported by neighboring edges that provide protection. We calculate the minimum sum of these assigned labels, called the Edge Modern Roman domination number, for some standard and known graphs. Furthermore, we investigate the behavior of this parameter under some certain graph operations such as the corona product and the Cartesian product.