It may be desirable to reduce the number of active nodes (such as routers) in a computer or communication network design while maintaining the ability of all devices to connect with one another. It is possible to establish the least number of active nodes essential for complete network connectivity by applying the concepts of Roman dominion. The act of assigning labels or tokens to the vertices of a graph, where each vertex is either labeled (dominated) or adjacent to another labeled vertex, resulting in a Roman dominating set, is termed a Roman dominating function, abbreviated as RDF. The Roman domination parameter of a network refers to the minimum weight of such a dominating set. A mapping f from the node set to the values 0, 1, 2 that satisfies the requirement that each node u for having value zero is connected to at least one node v for which having the value two is considered a Roman domination on a network \(G = ({V},{E})\) . A Roman dominating function’s weight can be expressed as the sum of all the node’s weights. The Roman domination number of a graph G is the lowest weight of a function on Roman domination of G. Within this paper, we compute the Roman domination number for the r-dimensional fractal cubic network FCN(r), r consistently holds a value greater than or equal to one. Additionally, we substantiate the claim that the r-dimensional fractal cubic network qualifies as a Roman graph.