Proceedings of International Conference on Applied Innovation in IT  ·  2026/06/12  ·  Vol. 14  ·  Issue 4  ·  pp. 451–457
Fuzzy Completely Equiprime Graph of Nearring via Fuzzy Ideals
Hussain Ali Mueen and Ameer A. J. Al-Swidi
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Abstract
This paper investigates a class of fuzzy graphs associated with nearrings through the concept of c-equiprime fuzzy ideals. The relationships between the structural properties of these fuzzy graphs and different classes of fuzzy ideals are examined, and conditions under which the resulting graphs become identical are established. In addition, the study integrates concepts from fuzzy graph theory and algebraic structures to analyze the interaction between fuzzy ideals and closed-loop structures, providing a unified framework for their investigation. The applicability of the proposed approach is discussed in terms of improving the representation and analysis of algebraic structures. Furthermore, a new concept, referred to as the annihilator ideal, is introduced and its fundamental properties are investigated. The study also identifies the conditions required for the existence of fuzzy cliques within the proposed graph model. It is shown that when the underlying fuzzy ideal satisfies c-equiprime conditions in simple or integral nearrings, the corresponding fuzzy graph exhibits a star-graph structure. Moreover, sufficient conditions are established under which an induced subgraph forms a fuzzy clique. These results provide new theoretical insights into the interplay between fuzzy graph structures and nearring theory while extending the applicability of fuzzy algebraic models.
Keywords
Annihilator Ideal c-equiprime FI Clique Fuzzy Graph Fuzzy Ideal
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