Abstract

The Maximal Monopoly of Graphs

Ahmed Mohammed Naji and N. D. Soner

Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore, INDIA.

ABSTRACT

In a graph G = (V, E) , a subset D V(G) is said to be a monopoly set of G if any vertex vV - 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.

Keywords :Monopoly, Maximal Monopoly, Domination, Maximal Domination, Independent.

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