# A study on picture Dombi fuzzy graph

• Kartick Mohanta Department of Mathematics, National Institute of Technology Durgapur, India
• Arindam Dey 2Department of Computer Sciences and Engineering, Saroj Mohan Institute of Technology, Hooghly, India
• Anita Pal Department of Mathematics, National Institute of Technology Durgapur, India
Keywords: t-norm, s-norm, Picture Dombi Fuzzy Graph, Picture Fuzzy Graph, Union, Composition, Cartesian Product, Join, Complement, Homomorphism, Isomorphism

### Abstract

The picture fuzzy graph is a newly introduced fuzzy graph model to handle with uncertain real scenarios, in which a simple fuzzy graph and intuitionistic fuzzy graph may fail to model those problems properly. The picture fuzzy graph is used efficiently in real-world scenarios which involve several answers to these types: yes, no, abstain, and refusal. In this paper, the new idea of Dombi picture fuzzy graph is introduced. We also describe some operations on Dombi picture graphs, viz. union, join, composition, and cartesian product. In addition, we investigated many interesting results regarding the operations. The concept of complement and isomorphism of Picture dombi fuzzy graph is presented in this paper. Some important results on weak and co-weak isomorphism of Picture dombi fuzzy graphs are derived.

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Published
2020-09-30
How to Cite
Mohanta, K., Dey, A., & Pal, A. (2020). A study on picture Dombi fuzzy graph. Decision Making: Applications in Management and Engineering, 3(2), 119-130. https://doi.org/10.31181/dmame2003119m
Section
Regular articles