Indian Streams Research Journal

Volume : IV, Issue : X, November - 2014

BOUNDS ON DOMINATION IN ZERO DIVISOR GRAPH

Suhas P. Gade, None

DOI : 10.9780/22307850, By : Laxmi Book Publication

Abstract :

Let R be a commutative ring and let be the zero divisor graph of R. The zero divisor graph of a ring is the graph(simple) whose vertex set is the set of non zero zero divisor, and an edge is drawn between two distict vertices if their product is zero. For a graph , a set S is a dominating set of , if every vertex in is adjacent to some vertex in S. The minimum Cardinality of vertex in such a set is called the domination number of and is denoted by . In this paper many bounds on were obtained in terms of the elements of . Also its relations with other domination parameters were obtained.

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References :

1. I. Beck, Coloring of commutative rings, J. Algebra 116(1998), 208-226.
2. D.F. Anderson, P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217, No.2(1999), 434-447.
3. T. W. Haynes, S. T. Hedeniemi, P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York (1998).
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8. V. R. Kulli, Vishwa International Publications, Gulbarga-585103, India.
9. V. R. Kulli, Vishwa International Publications, Gulbarga-585103, India.
10. D.F. Anderson, P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217, No.2(1999), 434-447.
11. T. W. Haynes, S. T. Hedeniemi, P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York (1998).
12. I. Beck, Coloring of commutative rings, J. Algebra 116(1998), 208-226.
13. D.F. Anderson, P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217, No.2(1999), 434-447.
14. T. W. Haynes, S. T. Hedeniemi, P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York (1998).
15. V. R. Kulli, Vishwa International Publications, Gulbarga-585103, India.
16. D.F. Anderson, P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217, No.2(1999), 434-447.
17. T. W. Haynes, S. T. Hedeniemi, P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York (1998).
18. D.F. Anderson, P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217, No.2(1999), 434-447.
19. T. W. Haynes, S. T. Hedeniemi, P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York (1998).
20. I. Beck, Coloring of commutative rings, J. Algebra 116(1998), 208-226.
21. V. R. Kulli, Vishwa International Publications, Gulbarga-585103, India.
22. D.F. Anderson, P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217, No.2(1999), 434-447.
23. T. W. Haynes, S. T. Hedeniemi, P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York (1998).
24. V. R. Kulli, Vishwa International Publications, Gulbarga-585103, India.

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