A study on energy of an intuitionistic fuzzy graph

• Authors: D. Gunasekaran , R. Vijayalakshmi
• Languages of publication: EN

Abstracts

EN

Let Ĝ = (V, E, ϛ, η) be a simple intuitionistic fuzzy graph. In this article, the notion of energy of the fuzzy graph is expanded to the energy of an intuitionistic fuzzy graph. The adjacency matrix of an intuitionistic fuzzy graph has been determined and evaluated the energy of an intuitionistic fuzzy graph in terms of its adjacency matrix with suitable illustrative examples. We investigated some lower and upper bounds on the energy of an intuitionistic fuzzy graph.

Keywords

EN

Energy; Fuzzy graph; Intuitionistic fuzzy graph; Intuitionistic fuzzy set

Discipline

• PHYSICS: PHYSICS

• Publisher: Scientific Publishing House „DARWIN”
• Journal: World Scientific News
• Year: 2019
• Volume: 136
• Pages: 134-147

Contributors

author

D. Gunasekaran

• PSG College of Arts and Science, Coimbatore, Tamil Nadu, India

author

R. Vijayalakshmi

• PSG College of Arts and Science, Coimbatore, Tamil Nadu, India

References

• [1] Atanassov K. T. Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20 (1986) 87-96.
• [2] Atanassov K.T. Intuitionistic fuzzy sets: Theory and Applications, Springer-Verlag, Heidelberg, 1999.
• [3] Anjali N, Mathew S, Energy of a fuzzy graph, Annals Fuzzy Mathematics and Informatics 6 (2013) 455-465.
• [4] R. Balakrishnan, The energy of a graph, Linear Algebra Appl 387 (2004) 287-295.
• [5] D. M. Cvetkovic and I. Gutman, Applications of Graph spectra, Math. Inst. Belgrade, 2009.
• [6] D.M. Caporossi, D. Cvetkovic, I.Gutman , P.Hansen, Variable neighborhood search for extremal graphs, 2. Finding graphs with extremal energy, J. Chem. Inf. Comput. Sci. 39 (1999) 984-996
• [7] I. Gutman, The energy of a graph, Ber. Math. Statist, Sekt. Forschungszentram Graz. 103 (1978), 1-22.
• [8] H. Liu, M. Lu, and F. Tian, Some upper bounds for the energy of graphs. J. Math. Chem. 41 (2007) 45-57.
• [9] R. Parvathi, M. G. Karunambigai, and K. T. Atanassov, Operations on Intuitionistic fuzzy graphs, Fuzzy Systems, 2009, FUZZ – IEEE 2009. IEEE International Conference, 1396-1401.
• [10] R. Parvathi, M. G. Karunambigai, Intuitionistic fuzzy graphs, Journal of Computation Intelligence: Theory and Applications (2006) 139-150.
• [11] J. Shao, F. Gong and Z. Du, Extremal energies of weighted trees and forest with fixed total weight sum, MATCH Commun. Math. Comput. Chem. 66 (2011) 879-890.
• [12] Rosenfeld A., Fuzzy graphs, Fuzzy Sets and their Applications (L. A. Zadeh, K. cS. Fu, K. Tanaka and M. Shimura, Eds.) Fuzzy sets and their applications to cognitive and decision process, Academic Press, New York (1975) 77-95.
• [13] R. J. Wilson, History of Graph Theory, in: Jonathan L. Gross, Jay Yellen (Eds.), Handbook of Graph Theory, CRC Press. 2004.
• [14] L.A. Zadeh, Fuzzy sets. Information and Computation 8 (1965) 338-353

• Document Type: article