In a graph G = (V;E), a set D ⊆V (G) is said to be a monopoly set of G if every vertex v ∈V-D has at least d(v)/ 2 neighbors in D. The monopoly size of G, denoted mo(G), is the minimum cardinality of a monopoly set among all monopoly sets in G. The set D ⊆ V (G) is an independent monopoly set in G if it is both a monopoly set and an independent set in G. The number of vertices in a minimum independent monopoly set in a graph G is the independent monopoly size of G and is denoted by imo(G). In this paper, we study the existence of independent monopoly set in graphs, bounds for imo(G), and some exact values for some standard graphs are obtained. Finally we characterize all graphs of order n with imo(G) = 1; n - 1 and n.
Naji, Ahmed M. and Soner, N. D.
Independent Monopoly Size In Graphs,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 10,
2, Article 6.
Available at: https://digitalcommons.pvamu.edu/aam/vol10/iss2/6