Fuzzy Subgroup-Based Centralizer-Graph
Elahe Mohammadzadeh
1
(
Department of Mathematics, Payame Noor University, Tehran, Iran.
)
Mohammad Hamidi
2
(
Department of Mathematics, Payame Noor University, Tehran, Iran.
)
Somayeh Amirmofidi
3
(
Department of Mathematics, Payame Noor University, Tehran, Iran.
)
کلید واژه: Centralizer-graph, Fuzzy subgroupiod, Good nilpotent fuzzy group, Dominating set.,
چکیده مقاله :
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.
چکیده انگلیسی :
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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