2 – Bondage Number of a Fuzzy Graph
Abstract
In this paper, 2-bondage set of a fuzzy graph G is dened. The2-bondage number, b2(G) is the minimum cardinality among all 2-bondage sets of G. The condition for a 2-bondage set of a fuzzy graph to be a bondage set is also given. The exact values of b2(G) is determined for several classes of fuzzy graphs.
References
[1] C. Berge. Graphs and Hypergraphs, American Elsevier Pub. Co; Revised edition (1973).
[2] E. J. Cockayne and S. Hedetniemi. Towards a theory of Domination in Graphs, Networks, 7(3)(1977), 247--261.
[3] J. F. Fink, M. S. Jacobson, L. F. Kinch and J. Roberts. The bondage number of a graph, Discrete Math., 86(1-3)(1990), 47--57.
[4] M. Krzywkowski. 2-bondage in graphs, Inter. J. Comp. Math., 90(7)(2013), 1358--1365.
[5] A. Nagoor Gani and V. T. Chandrasekaran. Domination in Fuzzy Graph, Advances in Fuzzy Sets and Systems, 1(1)(2006), 17--26.
[6] A. Nagoor Gani and P. Vadivel. A study on Domination, Independence domination and Irrenundance in Fuzzy Graph, Applied Math. Sci., 5(47)(2011), 2317--2325.
[7] A. Nagoor Gani, K. Prasanna Devi and M. Akram, Bondage And Non-Bondage Number of a Fuzzy Graph, International Journal of Pure and Applied Mathematics, Vol. 103, No.
2 (2015), 215--226.
[8] A. Nagoor Gani and K. Prasanna Devi. Edge Domination and Independence in Fuzzy Graphs, Advances in Fuzzy Sets and Systems, 15(2)(2013), 73--84.
[9] A. Nagoor Gani and K. Prasanna Devi. 2-Domination in Fuzzy Graphs, Intern. J. Fuzzy Mathematical Archive, 9(1)(2015), 119--124.
[10] O. Ore. Theory of graphs, Amer. Math. Soc. Colloq. Publi., Amer. Math. Soc, Providence, RI, (1962).
[11] A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and their Applications to Cognitive and Decision Processes,Proc. U.S.-Japan Sem., Univ. Calif.(1974), Berkeley,Calif., Academic Press, New York, (1975),77--95.
[12] A. Somasundaram, ,S. Somasundaram, Domination in Fuzzy Graphs--I, Pattern Recognition Letters, 19(9)(1998), 787--791.
[13] L. A. Zadeh. Fuzzy Sets, Information and Control, 8(3)(1965), 338--353.
[2] E. J. Cockayne and S. Hedetniemi. Towards a theory of Domination in Graphs, Networks, 7(3)(1977), 247--261.
[3] J. F. Fink, M. S. Jacobson, L. F. Kinch and J. Roberts. The bondage number of a graph, Discrete Math., 86(1-3)(1990), 47--57.
[4] M. Krzywkowski. 2-bondage in graphs, Inter. J. Comp. Math., 90(7)(2013), 1358--1365.
[5] A. Nagoor Gani and V. T. Chandrasekaran. Domination in Fuzzy Graph, Advances in Fuzzy Sets and Systems, 1(1)(2006), 17--26.
[6] A. Nagoor Gani and P. Vadivel. A study on Domination, Independence domination and Irrenundance in Fuzzy Graph, Applied Math. Sci., 5(47)(2011), 2317--2325.
[7] A. Nagoor Gani, K. Prasanna Devi and M. Akram, Bondage And Non-Bondage Number of a Fuzzy Graph, International Journal of Pure and Applied Mathematics, Vol. 103, No.
2 (2015), 215--226.
[8] A. Nagoor Gani and K. Prasanna Devi. Edge Domination and Independence in Fuzzy Graphs, Advances in Fuzzy Sets and Systems, 15(2)(2013), 73--84.
[9] A. Nagoor Gani and K. Prasanna Devi. 2-Domination in Fuzzy Graphs, Intern. J. Fuzzy Mathematical Archive, 9(1)(2015), 119--124.
[10] O. Ore. Theory of graphs, Amer. Math. Soc. Colloq. Publi., Amer. Math. Soc, Providence, RI, (1962).
[11] A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and their Applications to Cognitive and Decision Processes,Proc. U.S.-Japan Sem., Univ. Calif.(1974), Berkeley,Calif., Academic Press, New York, (1975),77--95.
[12] A. Somasundaram, ,S. Somasundaram, Domination in Fuzzy Graphs--I, Pattern Recognition Letters, 19(9)(1998), 787--791.
[13] L. A. Zadeh. Fuzzy Sets, Information and Control, 8(3)(1965), 338--353.
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2017-03-01
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