Advances and Applications in Discrete Mathematics

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SOME PROPERTIES OF TENSOR PRODUCT OF INTUITIONISTIC $L$-FUZZY GRAPHS

Authors

  • Tintumol Sunny
  • Sr. Magie Jose
  • Pramada Ramachandran

Keywords:

tensor product of intuitionistic $L$-fuzzy graphs, $L$-fuzzy degree of a vertex of an ILFG, regular ILFG, $L$-fuzzy degree of a vertex in tensor product.

DOI:

https://doi.org/10.17654/0974165822015

Abstract

In this paper, we define the tensor product of two intuitionistic L-fuzzy graphs (ILFGs) and study some of their basic properties. We show that the tensor product of two strong ILFGs is again a strong ILFG. Moreover, we introduce regular intuitionistic L-fuzzy graphs and discuss some of their properties and determine some conditions for the tensor product of two ILFGs to be regular.

Received: October 6, 2021
Accepted: December 27, 2021

References

K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1) (1986), 87-96.

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A. Kaufmann, Introduction a la Theorie des Sous-emsembles Flous, Masson et Cie 1, 1973.

A. Nagoor Gani and S. Shajitha Begum, Regular properties of fuzzy graph, Bull. Pure Appl. Sci. 27E(2) (2008), 415-423.

A. Nagoor Gani and S. Shajitha Begum, Degree, order and size in intuitionistic fuzzy graphs, International Journal of Algorithms, Computing and Mathematics 3(3) (2010), 11-16.

A. Nagoor Gani and S. Shajitha Begum, Totally regular property of Cartesian product of intuitionistic fuzzy graphs, Advances in Fuzzy Mathematics 12(1) (2017), 63-76.

A. Nagoor Gani and S. Shajitha Begum, Some composition properties on totally regular intuitionistic fuzzy graphs, Bull. Pure Appl. Sci. 38E(1) (2019), 253-263.

R. Pramada and K. V. Thomas, On isomorphisms of L-fuzzy graphs, Annals of Fuzzy Mathematics and Informatics 11(2) (2016), 301-313.

K. Radha and M. Vijaya, The total degree of a vertex in some fuzzy graphs, Jamal Academic Research Journal 1 (2014), 160-168.

K. Radha and M. Vijaya, Totally regular property of the composition of two fuzzy graphs, International Journal of Pure and Applied Mathematical Sciences 8(1) (2015), 87-100.

A. Rosenfeld, Fuzzy Graphs. Fuzzy Sets and their Applications, Academic Press, New York, 1975, pp. 77-95.

Tintumol Sunny, Pramada Ramachandran and Sr. Magie Jose, On level subsets of intuitionistic L-fuzzy graphs, Malaya Journal of Matematik 8(4) (2020), 1942-1946.

J. P. Tremblay and R. Manohar, Discrete Mathematical Structures with Applications to Computer Science, Tata McGraw-Hill, New Delhi, 1997.

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Published

2022-03-09

Issue

Vol. 30 (2022)

Section

Articles

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How to Cite

SOME PROPERTIES OF TENSOR PRODUCT OF INTUITIONISTIC $L$-FUZZY GRAPHS. (2022). Advances and Applications in Discrete Mathematics, 30, 1-18. https://doi.org/10.17654/0974165822015

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