Fuzzy Subgroup-Based Centralizer-Graph

Elahe Mohammadzadeh ¹ ( )
Mohammad Hamidi ² ( )
Somayeh Amirmofidi ³ ( )

Submited date : 2024-12-04 Accepted date : 2025-06-12

Keywords: Centralizer-graph, Fuzzy subgroupiod, Good nilpotent fuzzy group, Dominating set.,

Abstract :

In this paper, we introduce the notion of (non)commutative fuzzy subgroup-based centralizer-graph with respect to any given non-abelian group. Basically, we investigate on dominating set of the class of (non)commutative fuzzy subgroup-based centralizer-graphs. Also, with some additional conditions we see that the (non)commutative fuzzy subgroup-based centralizer-graphs are connected. Also, we investigate on isomorphic (non)commutative fuzzy subgroup-based centralizer-graphs and make a new isomorphic graph of (non)abelian groups derived from an isomorphic (non)commutative fuzzy subgroup-based centralizer-graph. Also, we see that if any given underlined fuzzy subset is an extra-special fuzzy subgroup, then the related fuzzy subgroup-based centralizer-graphs are isomorphic and if any given underlined fuzzy subset is good nilpotent of class 2, then it is an extra-special fuzzy subgroup.

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