A subset M ⊆ V (G) of a graph G(V,E) is referred to be a monopoly set of G if each vertex v ∈ V − M has at least
one neighbor in M. The smallest cardinality of a monopoly set among all monopoly sets in G is its monopoly
size, or mo(G). In this study, we determine the minimal monopoly energies of various typical graphs and introduce
the minimum monopoly energy, or EM(G), of a graph G. We define upper and lower limits for EM(G).