Structural Properties of N-Fuzzy Graphs with Applications to Bridges, Cut Nodes, and Trees

Wajid Ali; Iftikhar Ul Haq; Usman Ghani; Amal Kumar Adak

Authors

Wajid Ali School of Computer Science and Artificial Intelligence, Duy Tan University, Danang, 550000, Vietnam. https://orcid.org/0000-0002-4926-722X Author
Iftikhar Ul Haq Department of Mathematics, Air University Islamabad, Islamabad, Pakistan. https://orcid.org/0000-0002-1043-5820 Author
Usman Ghani Department of Mathematics, Air University Islamabad, Islamabad, Pakistan. https://orcid.org/0000-0002-4124-6432 Author
Amal Kumar Adak Department of Mathematics, Ganesh Dutt College, Begusarai, India. https://orcid.org/0000-0002-3644-782X Author

Keywords:

N-fuzzy graph; N-fuzzy bridge; N-fuzzy cut node; N-fuzzy tree; Strongest path; Maximum spanning tree

Abstract

In this paper, we study several structural properties of N-fuzzy graphs. Fundamental concepts including N-fuzzy sets, N-fuzzy relations, N-fuzzy bridges, N-fuzzy cut nodes, N-fuzzy cycles, and N-fuzzy trees are reviewed and analyzed. The relationships among these concepts are investigated through theoretical results and illustrative examples. In particular, we examine conditions involving N-fuzzy bridges and N-fuzzy cut nodes and provide counterexamples showing that certain converse statements do not hold in general. Furthermore, properties of N-fuzzy trees are discussed and characterized using strongest paths and maximum spanning trees. The obtained results contribute to the understanding of the structural behavior of N-fuzzy graphs and provide a basis for future research in N-fuzzy network analysis and related applications.