Secure domination in fuzzy graphs and intuitionistic fuzzy graphs
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In this paper we introduce the concept of secure domination and secure total domination in fuzzy graphs and intuitionistic fuzzy graphs. Secure domination number $\gamma_{s}(G)$ and secure total domination number $\gamma_{st}(G)$ for several classes of fuzzy graphs and intuitionistic fuzzy graphs have been determined. The definition of 2-total dominating set, 2-secure dominating set, 2-secure total dominating set and its domination number in fuzzy graphs and intuitionistic fuzzy graphs are defined and some properties are analysed with suitable examples.
Abstract
In this paper we introduce the concept of secure domination and secure total domination in fuzzy graphs and intuitionistic fuzzy graphs. Secure domination number $\gamma_{s}(G)$ and secure total domination number $\gamma_{st}(G)$ for several classes of fuzzy graphs and intuitionistic fuzzy graphs have been determined. The definition of 2-total dominating set, 2-secure dominating set, 2-secure total dominating set and its domination number in fuzzy graphs and intuitionistic fuzzy graphs are defined and some properties are analysed with suitable examples.
참고문헌 (21)
- M. Akram, "Novel applications of bipolar fuzzy graphs to decision making problems", Journal of Applied Mathematics and Computing, pp.1~19 (2016)
- M. Akram, "Certain types of domination in m-polar fuzzy graphs", Journal of Multivalued and Soft Computing, 32 (2017)
- G. Amerkhan, "Secure connected domination in a graph", International Journal of Mathematical Analysis, 8(42), pp.2065~2074 (2014)
- K. T. Atanassov, "Intuitionistic fuzzy sets" (1983), Sofia
- K. T. Atanassov, "Intuitionistic fuzzy sets", Fuzzy sets and Systems, 20, pp.87~96 (1986)
- C. Berge, "Graphs and hypergraphs" (1973), North Holland Amsterdam
- E. J. Cockayne, "Secure domination, weak roman domination and forbidden subgraphs", Bulletin of the Institute of Combinatorics and its Applications, 39, pp.87~100 (2003)
- M. G. Karunambigai, "Some properties of a regular intuitionistic fuzzy graph", International Journal of Mathematics and Computation, 26(4), pp.53~61 (2015)
- M. G. Karunambigai, "Degrees in intuitionistic fuzzy graphs", Ann. Fuzzy Math. Inform, 13(1), pp.1~13 (2017)
- H. B. Merouane, "On secure domination in graphs", Information Processing Letters, 115, pp.786~790 (2015)
- J. N. Mordeson, "Fuzzy graphs and fuzzy hypergraphs" (2001), Physica Verlag
- A. Nagoorgani, "Domination in fuzzy graph", Advances in fuzzy sets and system, 1(1), pp.17~26 (2006)
- A. Nagoorgani, "Degree, order and size in intuitionistic fuzzy graphs", International Journal of Algorthms, Computing and Mathematics, 3, pp.11~16 (2010)
- A. Nagoor Gani, "2-domination in fuzzy graphs", International Journal Fuzzy Mathematical Archive, 9(1), pp.119~124 (2015)
- O. Ore, "Theory of graphs", American Mathematical Society Colloquium Publications, 38 (1962)
- R. Parvathi, "Intuitionistic fuzzy graphs", Computational Intelligence, Theory and applications, pp.139~150 (2006)
- R. Parvathi, "Operations on intuitionistic fuzzy graphs", Proceedings of IEEE International Conference Fuzzy Systems (FUZZ-IEEE), pp.1396~1401 (2009)
- R. Parvathi, "Domination in intuitionistic fuzzy graphs", Notes on Intu-itionistic Fuzzy Sets, 16, pp.39~49 (2010)
- R. Parvathi, "Some results on domination number in products of intu-itionistic fuzzy graphs", Ann. Fuzzy Math. Inform, 9(3), pp.403~419
- A. Somasundaram, "Domination in fuzzy graphsuI", Pattern Recognition Letters, 19(9), pp.787~791 (1998)
- L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)