Author
S Keerthana, E.Mynavathi
Keywords
Fuzzy Graph; Fuzzy Connectivity; Strong Fuzzy Graph; Fuzzy Path; Graph Theory.
Abstract
Fuzzy graph theory is an important extension of classical graph theory introduced to model systems involving uncertainty. In fuzzy graphs, vertices and edges are associated with membership values between 0 and 1. Connectivity is one of the most fundamental structural properties of fuzzy graphs. It helps in understanding the relationship between vertices and the strength of connections between them. In this paper, various types of connectivity in fuzzy graphs are studied. Important definitions, properties, and theorem results related to fuzzy connectivity and strong fuzzy connectivity are presented. The structural properties of connected fuzzy graphs are analyzed. These results help in understanding fuzzy networks and their applications in real-world systems.
References
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R. Balakrishnan and K. Ranganathan, A Textbook of Graph Theory, 2nd ed. Springer, 2012.
[2] M. S. Sunitha, “Connectivity in a fuzzy graph and its complement,” International Journal of Fuzzy Systems, vol. 12, no. 3, pp. 116–125, 2016.
[3] T. Pathinathan and J. Jesintha Rosline, “Characterization of fuzzy graphs into different categories using arcs in fuzzy graphs,” International Journal of Fuzzy Systems, vol. 12, no. 3, pp. 18–34, 2016.
[4] M. S. Sunitha and S. Mathew, “Fuzzy Graph Theory: A Survey,” International Journal of Fuzzy Systems, vol. vol. 12, no. 3, pp. 234–257, 2016.
[5] M. Muthukani, “Connectivity in a fuzzy graph,” International Journal of Fuzzy Systems, vol. 12, no. 3, pp. 56–81, 2016.
[6] R. J. Wilson, Introduction to Graph Theory, 4th ed. Pearson Education Limited, 2010.
[7] S. K. Yadav, Elements of Graph Theory, Krishna Prakashan Media, 2013.
[8] V. K. Balakrishnan, Graph Theory, McGraw-Hill Education, 2012
[9] S. Arumugam and S. Ramachandran, Invitation to Graph Theory, Scitech Publications, 2011.
R. Balakrishnan and K. Ranganathan, A Textbook of Graph Theory, 2nd ed. Springer, 2012.
Accepted : 11 April 2026
Published : 15 April 2026
DOI: 10.30726/esij/v13.i2.2026.132008