Algebraic Structures and Their ApplicationsAlgebraic Structures and Their Applications
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Feed provided by Algebraic Structures and Their Applications. Click to visit.Results on Engel Fuzzy Subgroups
http://as.yazd.ac.ir/article_1137_212.html
‎In the classical group theory there is‎ an open question‎: ‎Is every torsion free n-Engel group (for n ≥ 4)‎, nilpotent?‎. ‎To answer the question‎, ‎Traustason‎ [11] showed that with some additional conditions all‎ ‎4-Engel groups are locally nilpotent‎. ‎Here‎, ‎we gave some partial‎ answer to this question on Engel fuzzy subgroups‎. ‎We show that if μ is a normal 4-Engel fuzzy‎ subgroup of group G‎, ‎x,y in G and a =yx‎, ‎then μ|< a‎, ‎y‎‎> is a generalized nilpotent of class at‎ most 2‎. ‎Also we define a torsion free fuzzy subgroup and show‎ ‎that if μ is a 4-Engel torsion free fuzzy subgroup of G‎, ‎then μ|< a‎, ‎y‎‎> is a generalized nilpotent of class at most 4‎, ‎for conjugate elements a,y in G‎. Tue, 31 Oct 2017 20:30:00 +0100On the zero forcing number of some Cayley graphs
http://as.yazd.ac.ir/article_1138_212.html
‎Let Γa be a graph whose each vertex is colored either white or black‎. ‎If u is a black vertex of Γ such that exactly one neighbor‎ ‎v of u is white‎, ‎then u changes the color of v to black‎. ‎A zero forcing set for a Γ graph is a subset of vertices Zsubseteq V(Γ) such that‎ if initially the vertices in Z are colored black and the remaining vertices are colored white‎, ‎then Z changes the color of all vertices Γ in to black‎. ‎The zero forcing number of Γ is the minimum of |Z| over all zero forcing sets for Γ and is denoted by Z(Γ)‎. In this paper‎, ‎we consider the zero forcing number of some families of Cayley graphs‎. ‎In this regard‎, ‎we show that Z(Cay(D2n,S))=2|S|-2‎, ‎where D2n is dihedral group of order 2n and S={a‎, ‎a3‎, ‎... ‎, ‎a2k-1‎, ‎b}. ‎Also‎, ‎we obtain Z(Cay(G,S))‎, ‎where G=< a> is a cyclic group of even order n and S={ai :‎ 1≤ i≤ n‎ and i is odd}‎, ‎S={ai‎ :‎1≤ i≤ n‎ and i is odd}{ak,a-k} or |S|=3‎.Tue, 31 Oct 2017 20:30:00 +0100On the eigenvalues of non-commuting graphs
http://as.yazd.ac.ir/article_1140_212.html
The non-commuting graph $Gamma(G)$ of a non-abelian group $G$ with the center $Z(G)$ is a graph with thevertex set $V(Gamma(G))=Gsetminus Z(G)$ and two distinct vertices $x$ and $y$ are adjacent in $Gamma(G)$if and only if $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.Tue, 31 Oct 2017 20:30:00 +0100