Department of Studies in Mathematics,
University of Mysore, Manasagangotri, Mysore, INDIA.
ABSTRACT
In a graph G = (V, E) , a subset D ÍV(G) is said to be a monopoly
set of G if any vertex vÎV - D has at least
2
d(v)
neighbors in D, where
d(v) is dgree of v in G . A monopoly set D of G is called a maximal
monopoly set of G if V - D is not a monopoly set in G , by the maximal
monopoly size of G , we mean the smallest cardinality of a maximal monopoly set
in G , denoted by Mo(G) . In this paper, we introduce and study the concept of
maximal monopoly size in graphs. We investigate the relationship between maximal
monopolies size and some parameters of graphs. Bounds on Mo(G) and exact
values for some standard graphs are found.
Mathematics Subject Classification : 05C69, 05C38, 05C99.
