Naji, A. M. and Soner, N. D.
(2015)
*Independent monopoly size in graphs.*
Applications and Applied Mathematics-An International Journal, 10 (2).
pp. 738-749.
ISSN 1932-9466

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## Abstract

In a graph G = (V, E), a set D subset of V (G) is said to be a monopoly set of G if every vertex v is an element of 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 subset of 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.

Item Type: | Article |
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Uncontrolled Keywords: | Vertex degree; monopoly set of a graph; independent monopoly set of a graph; independent monopoly size of a graph |

Subjects: | E Mathematical Science > Mathematics |

Divisions: | Department of > Mathematics |

Depositing User: | Shrirekha N |

Date Deposited: | 29 May 2019 06:40 |

Last Modified: | 17 Sep 2019 10:03 |

URI: | http://eprints.uni-mysore.ac.in/id/eprint/615 |

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