Some Operations on Complex Fuzzy Graphs

Azhagendran N, Mohamed Ismayil A


In this paper we discussed about some types of complex fuzzy
graphs which is the extension of fuzzy graph. As the membership
value of elements of fuzzy graph is in between 0 and 1. In complex
fuzzy graph it will be extended to unit circle of complex plane. Some
operations such as union, intersection, composition, cartesian product
of two complex fuzzy graphs are introduced. Some basic theorems
with respect to the above mentioned operations are proved with examples.


Complex fuzzy graph; Union; Intersection; Composition; Cartesian product

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Bhattacharya.P. Some remarks on fuzzy graphs. Pattern recognition Lett.6, pages

–302, 1987.

Daniel Ramot, Friedma.M,Langholz, RonMilo and Abraham.Kandel. Complex

fuzzy sets. IEEE transactions on fuzzy systems, 10(2):171–186, 2002.

Harary. Graph Theory. Addition wesley, London, 1969.

Mordeson.J.N and Peng.C.S. Operations on fuzzy graphs. Information Sci., 79:

–170, 1994.

Nagoorgani.A and Basheer.Ahamed.M. Order and size in fuzzy graph. Bulletin

of pure and applied sciences, 22E(1):145–148, 2003.

Nagoorgani.A and Latha.R. Some properties on operations of fuzzy graphs. Advances in Fuzzy sets and Systems, 19(1):1–24, 2015.

Naveed.Yaqoob, Muhammad.Gulistan, Seifedine kadry and Hafiz.Abdul.Wahab.

Complex intuitionistic fuzzy graphs with applications in cellular network

provider companies. Mathematics, 7(35):1–18, 2019.

Rosenfeld.A, Zadeh.L.A and M.Shimura.Eds. Fuzzy graph in fuzzy sets and their

applications. pages 77–95, 1975.

Shannon.A and Atanassov.K. A first step to a theory of the intuitionistic fuzzy

graph. In the First workshop on Fuzzy Based Expert system ( D.Lakov, Ed.),

pages 59–61, 1994.

Thirunavukarasu.P, Suresh.R and Viswanathan.K.K. Energy of a complex fuzzy

graph. International journal of math. science and Engg. Appls (IJMSEA), 10

(1):243–248, 2016.

Xueling Ma, Jianming Zhan, Madad Khan, Muhammad Zeeshan, Saima Anis,

Abdul Sami Awan Complex fuzzy sets with applications in signals. computational and applied mathematics, 38(150):1–34, 2019.

L.A.Zadeh Fuzzy sets. Information and Control,8(3):338–353, 1965.



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