Roman rule numbers are widely studied as a variation of rule numbers on graphs. Given a graph $G=(V,E)$, the dominant number of the graph is the minimum vertex set size $V’ \subseteq V$ and every vertex in the graph is either $V’$ will be or adjacent to a vertex of $V’$. The Roman dominance function of $G$ is defined as $f:V \rightarrow \{0,1,2\}$ such that all vertices with label 0 in $G$ are adjacent to vertices with label 2 will be The Roman domination number of the graph is the minimum summed weight of all possible Roman domination functions. In this paper, we focus and analyze a new subspecies, the n-attack Roman rule, specifically his 2-attack Roman rule (n = 2)$. The $n$ attack Roman dominance function of $G$ is defined similarly to the Roman dominance function, except that for any $j\leq n$ the subset $S$ of $j$ vertices is all labeled 0. Additional conditions apply. An open neighborhood of $S$ must have at least $j$ vertices with label 2. The $n$ attacking Rome dominance number is the minimum summed weight of all possible $n$ attacking Rome domination functions. 2 Introduces the algorithm and properties for determining the number of attacks Rome conquered. We also look at how to use a Python program to place dominant vertices when only a finite number of vertices are allowed. Finally, we describe the number of double-strike Roman rulers of infinite regular graphs tiling planes. Finally, we discuss open questions and possible ways to extend these results to the common $n$ attack case.
