Dominating Energy of Operations on Intuitionistic Fuzzy Graphs
-
2018-10-02 https://doi.org/10.14419/ijet.v7i4.10.20928 -
Intuitionistic fuzzy Graph, complements, union, Join of two intuitionistic fuzzy Graph. -
Abstract
The concept of energy of an Intuitionistic Fuzzy Graph is extended to dominating Energy in operations on Intuitionistic Fuzzy Graph. In this paper, We have obtained the value of dominating Energy in different operations such as complement, Union, Join, Cartesian product and composition between two intuitionistic Fuzzy graphs. Also we study the relation between the dominating Energy in the operations on two Intuitionistic Fuzzy Graphs.
Â
Â
-
References
[1] Anjali.N, Sunil Mathew, Energy of a fuzzy graph of Annals of Fuzzy Mathematics and Informatics, (2013).
[2] Atanassov.K, Intuitionistic fuzzy sets, Fuzzy sets and systems, 20, 87-96, (1986).
[3] Atanassov.K, Intuitionistic Fuzzy sets : Theory and Applications, Springer-Verlag, Heidelberg, (1999).
[4] Cockayne.E.J and Hedetnieme, S.T, Towards a Theory of Domination in Graphs, Networks 7, 247-261, (1977).
[5] De Jaenisch,C.F. Applications de l’ Analyze Mathematique an Jen des Echecs, (1862).
[6] Deepa.G, Praba.B,Chandrasekaran.V.M,Virus Spread in an Intuitionistic Fuzzy Network of International Journal of Applied Engineering Research,Vol.9, No.16, pp.5507- 5515(2014).
[7] Deepa.G, Praba.B, Chandrasekaran.V.M, Max-Min Intuitionistic Fuzzy Matrix of an Intuitionistic Fuzzy Graph,International Journal of Pure and Applied Mathematics, Vol.98, No.3, 375-387,(2015).
[8] Gutman,I. The Energy of a Graph, Ber. Math - Statist. Sekt. Forschungsz. Graz, 103, 1-22 ,(1978).
[9] Gutman.I, The energy of a graph: old and new results, in Algebraic Combinatorics and Applications, A. Betten, A. Kohner, R. Laue, and A.Wassermann, eds., Springer, Berlin, 196-211 (2001).
[10] Nagoorgani.A and Chandrasekaran.V.T, Domination in Fuzzy Graph, Advances in Fuzzy Sets and systems, 1(1),17-26 (2006).
[11] Parvathi R, Karumbigai M G. Intutionistic fuzzy graphs. Computational Intelligence,Theory and Applications. 139- 150.
[12] Parvathi R and G. Thamizhendhi, Domination in intuitionistic fuzzy graphs, Fourteenth Int. Conf. on IFSs, Sofia, 15-16 May 2010 ,NIFS Vol. 16 (2010), 2, 39-49
[13] Praba.B, Chandrasekaran.V.M., Deepa.G, Energy of an Intuitionistic Fuzzy Graph of Italian journal of pure and applied mathematics-N.32,431-444, (2014).
[14] Rosenfeld.A, Fuzzy Graphs, in Zadeh.L.A, Fu. K.cS, Tanaka.K and Shimura.M (eds.), Fuzzy Sets and their Applications to Cognitive and Decision Process, Academic Press, New York, 75-95 (1975).
[15] Somasundaram.A and Somasundaram.S, Domination in Fuzzy Graphs – I, Elsevier Science, 19, 787-791 (1998).
[16] Sharief Basha.S and E. Kartheek, Laplacian Energy of an Intuitionistic Fuzzy Graph, Indian Journal of Science and Technology, ,Vol 8(33),1-7 , (Dec2015).
[17] Vinoth Kumar.N, Geetha Ramani.G, Some Domination Parameters of the Intuitionistic Fuzzy graph and its Properties, International Journal of Mathematics and Scientific .Compting, Vol.1, No.1, (2011).
Zadeh.L.A., Fuzzy sets , Information and Control, 1965;, 8: 338-353
-
Downloads
-
How to Cite
Kalimulla, A., Vijayaragavan, R., & Sharief Basha, S. (2018). Dominating Energy of Operations on Intuitionistic Fuzzy Graphs. International Journal of Engineering & Technology, 7(4.10), 328-335. https://doi.org/10.14419/ijet.v7i4.10.20928Received date: 2018-10-04
Accepted date: 2018-10-04
Published date: 2018-10-02