Consider a G=(V,E) and the function f :V -{0,1,2}. . Unguarded with regard to is defined as a node u with  f (u) = 0  that is not next to a node with 1 or 2 . The function f (V₀ ,V₁,V₂ ) fulfilling the condition, in which each node u for which f (u)=0 is adjoint to at least one node v to which f (v) =2 , is referred to be a Roman dominant function, known as RDF of a graph G . Roman domination number (RDN) of graph represented by r_R (G), is the bare lowest count of guards that must be employed in any RDF. In this paper, we introduce a new form for graph called Semi-Middle Graph for any given graph and we find the RDN for the Semi - Middle Graph of some specific graphs. In the field of networking, the concept of the Semi-Middle Graph can be applied to network topology optimization. Specifically, it can be used in the design of communication networks where each direct connection (edge) between two nodes (devices or routers) has an intermediary node that facilitates more efficient data routing or enhances fault tolerance. Usefulness of Roman Domination Number of a Semi-Middle Graph in Networking includes Network Coverage and Monitoring, Fault Tolerance and Redundancy, Optimal Placement of Relays and Routers, Load Balancing and Resource Allocation.