| Title of paper:
|
Regularity and duality of intuitionistic fuzzy k-partite hypergraphs
|
| Author(s):
|
| K. K. Myithili
|
| Department of Mathematics (CA), Vellalar College for Women, Erode-638012, Tamilnadu, India
|
| mathsmyth@gmail.com
|
| R. Keerthika
|
| Department of Mathematics, Vellalar College for Women, Erode-638012, Tamilnadu, India
|
| keerthibaskar18@gmail.com
|
|
| Presented at:
|
Proceedings of the International Workshop on Intuitionistic Fuzzy Sets, 15 December 2023, Banská Bystrica, Slovakia
|
| Published in:
|
Notes on Intuitionistic Fuzzy Sets, Volume 29 (2023), Number 4, pages 401–410
|
| DOI:
|
https://doi.org/10.7546/nifs.2023.29.4.401-410
|
| Download:
|
 PDF (340 Kb, File info)
|
| Abstract:
|
A graph in which the edge can connect more than two vertices is called a Hypergraph. A k-partite hypergraph is a hypergraph whose vertices can be split into k different independent sets. In this paper, regular, totally regular, totally irregular, totally neighborly irregular Intuitionistic Fuzzy k-Partite Hypergraphs (IFk-PHGs) are defined. Also order and size along with the properties of regular and totally regular IFk-PHGs are discussed. It has been proved that the size [math]\displaystyle{ S(\mathscr{H}) }[/math] of a r-regular IFk-PHG is [math]\displaystyle{ \frac{tr}{2} }[/math] where [math]\displaystyle{ t=\left|V\right| }[/math]. The dual IFk-PHG has also been defined with example.
|
| Keywords:
|
Total degree, Regular IFk-PHG, Totally regular IFk-PHG, Totally irregular IFk-PHG, Totally neighborly irregular IFk-PHG, Dual IFk-PHG.
|
| AMS Classification:
|
05C65.
|
| References:
|
- Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Physica - Verlag, New York, Berlin.
- Berge, C. (1976). Graphs and Hypergraphs, North - Holland, New York.
- Mordeson, J. N., & Nair, P. S. (2000). Fuzzy Graphs and Fuzzy Hypergraphs, Physica - Verlag, New York.
- Akram, M., Shahzadi, S., & Saeid, A. B. (2018). Single-Valued Neutrosophic hypergraphs, TWMS Journal of Applied and Engineering Mathematics, 8(1), 122–135.
- Myithili, K. K., & Keerthika, R. (2020). Types of Intuitionistic Fuzzy k-Partite Hypergraphs, AIP Conference Proceedings, 2261, 030012-1-030012-13.
- Myithili, K. K., & Keerthika, R. (2022). Isomorphic Properties on Intuitionistic Fuzzy k-Partite Hypergraphs, Advances and Applications in Mathematical Sciences, 21(7), 3653–3672.
- Nagoor, Gani A., & Radha, K. (2008). On Regular Fuzzy Graphs, Journal of Physical Sciences, 12, 33-40.
- Parvathi, R., Thilagavathi, S., & Karunambigai, M. G. (2009). Intuitionistic Fuzzy Hypergraphs, Bulgarian Academy of Sciences, Cybernetics and Information Technologies, 9(2), 46–53.
- Pradeepa, I., & Vimala, S. (2016). Regular and Totally Regular Intuitionistic Fuzzy Hypergraph, International Journal of Mathematics and its applications, 4(1-c), 137–142.
- Pradeepa, I., & Vimala, S. (2016). Properties of irregular Intuitionistic Fuzzy Hypergraphs, International Journal of Recent Scientific Research, 7(6), 11971–11975.
|
| Citations:
|
The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.
|
|
