چكيده
In this thesis, first we study commutators of a polygroup. Then for a finite polygroup P and a
fixed element g ∈ P, we introduce the g-graph Δg
P . In addition, we get a spanning subgroup of
Δg
P . Also, with some additional conditions we see that it is connected and diam(Δg
P ) ≤ 3. Then,
we investigate isomorphic graphs. Spesially, we prove that if A and B are two non-commutative
polygroups, with the same order and Δg
P
φ≃
Δh
H, then Δ(g,a)
P×A
≃ Δ(h,b)
H×B, where h = φ(g),
b = f(a) and F : A → B is a bijection map. Also, we show that if Δg
P
φ≃
Δh
H and P is
nilpotent, then H is nilpotent. Moreover, we study and obtain some results on Γ(g)(G), the noncommutative
fuzzy subgroup-based centralizer-graph ofG. Basically, we investigate on dominating
set of Γ(e)(G). Also, with some additional conditions we see that Γ(g)(G) is connected. Then,
we investigate on isomorphic fuzzy graphs and we make a new isomorphic graph of groups derived
from an isomorphic non-commutative fuzzy subgroup-based centralizer-graph. We see that if μ is
an extra special fuzzy subgroup, Γ(g)(G) ≃ Γν(h)(H) and ν is good nilpotent of class 2, then ν
is an extra-special fuzzy subgroup
