Fuzzy Graphs


  • Huda Mutab Al Mutab King Saud University




Fuzzy Graph, Irregular Fuzzy Graph, Regular Fuzzy Graph


In this paper, neighbourly irregular fuzzy graphs, neighbourly total irregular fuzzy graphs, highly irregular fuzzy graphs and highly total irregular fuzzy graphs are introduced. A necessary and sufficient condition under which neighbourly irregular and highly irregular fuzzy graphs are equivalent is provided. We define d2 degree of a vertex in fuzzy graphs and total d2 -degree of a vertex in fuzzy graphs and (2, k)-regular fuzzy graphs, totally (2, k)- regular fuzzy graphs are introduced. (2, k)- regular fuzzy graphs and totally (2, k)-regular fuzzy graphs are compared through various examples.


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Author Biography

Huda Mutab Al Mutab, King Saud University

Computer Science Department, College of Science and Human studies in Durma, Shaqra University, Saudi Arabia


A. Rosenfeld. : Fuzzy graphs, In: L. A. Zadeh, K. S. Fu, M. Shimura, EDs. .:Fuzzy Sets and Their Applications, Academic press (1975), pp. 77-95.

A. Nagoor Gani and K. Radha .:The degree of a vertex in some fuzzy graphs ,International Journal of algorithms, computing and Mathematics, 2(3), (2009), pp. 107-116.

A. Nagoor Gani and K. Radha. .: On Regular Fuzzy graphs, Journal of Physical Science, (12), (2008), pp. 33-40.

A. Nagoor Gani and M. Basheer Ahmed. .: Order and Size in fuzzy graph, Bulletin of pure and applied Sciences, 22E(1), (2003), pp. 145-148.

A. Nagoor Gani and S. R. Latha. .: On irregular fuzzy graphs, Appl. Math. Sci.6 (2012), pp. 33-44.

H. J. Zimmermann. : Fuzzy set Theory And its Applications, Second edition. Kluwer Academic Puplishers, Bosten, Dordrecht, London, (1990).

J. N. Mordeson and P. S. Nair. .: Fuzzy graphs and Fuzzy hypergraphs, Physica verlag, (2000).

K. H. Rosen .: Discrete Mathematic and Its Applications, Seventh Edition, McGraw Hill companies, America,New York , (2012).

K. Radha and N. Kumaravel. .: Some Properties of edge regular fuzzy graphs, Jamal Acad. Res. J. (2014), pp. 121-127.

K. R. Bhutani, and A. Rosenfeld. .: Fuzzy end nodes in fuzzy graphs, Information Sciences, (2003), pp. 319-322.

K. R. Sandeep Narayan and M. S. Sunitha .: Connectivity in a Fuzzy Graph and its Complement, Gen. Math. Notes, 9(1), (2012), pp. 38-43.

M. Hussain. .: Fuzzy Relations. Belking Institute of Technology School of Engineering Department of Mathematics and Science, (2010).

N. R. Santhi Maheswari and C. Sekar. .: On (2, k )-regular fuzzy graphs, G.Venkataswamy Naidu College, Kovilpatti- 628502, India, (2010).

N. R. Santhi Maheswair and C. Sekar. .: On neighbourly edge irregular fuzzy graphs, International Journal of Mathematical Archive 6 (10) (2015), pp. 224-231.

N. R. Santhi Maheswari and C. Sekar .: On strongly edge irregular fuzzy graphs. Kragu Jevac Journal of Math-ematics, Volume 40(1), (2016), pp. 125-135.

O. T. Manjusha, M. S. Sunitha .: Connected domination in fuzzy graphs using strong arcs, Annals of Fuzzy mathematics and Informatics, volume x, (2015), pp. 1-xx.

P. Bhattachara. .: Some Remarks on Fuzzy Graphs, Pattern Reconition Lett.6 (1987), pp. 297-302.

S. N. Sivanandam, S. Sumathi and S. N. Deepa. .: Introduction to Fuzzy Logic using MATLAB. Springer-verlag Berlin Heidelberg, (2007).

S. P. Nandhini and E. Nandhini. .: Strongly irregular fuzzy geaphs, International Journal of Algorithms, Computing and Mathematics 2 (3) (2009), pp. 107-116.




How to Cite

Al Mutab, H. M. . (2019). Fuzzy Graphs. JOURNAL OF ADVANCES IN MATHEMATICS, 17, 232–247. https://doi.org/10.24297/jam.v17i0.8443