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The Main Eigenvalues of the Undirected Power Graph of A Group
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نویسنده
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Javarsineh Mehrnoosh ,Fath-Tabar Gholam Hossein
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منبع
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Journal Of Algebraic Structures And Their Applications - 2017 - دوره : 4 - شماره : 1 - صفحه:19 -32
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چکیده
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The undirected power graph of a finite group g, p (g), is a graph with the group elements of g as vertices and two vertices are adjacent if and only if one of them is a power of the other. let a be an adjacency matrix of p (g). an eigenvalue λ of a is a main eigenvalue if the eigenspace ε(λ) has an eigenvector x such that xtj ≠ 0, where j is the all-one vector. in this paper we want to focus on the power graph of the finite cyclic group zn and find a condition on n where p (zn) has exactly one main eigenvalue. then we calculate the number of main eigenvalues of p (zn) where n has a unique prime decomposition n = pr p2. we also formulate a conjecture on the number of the main eigenvalues of p (zn) for an arbitrary positive integer n.
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کلیدواژه
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Power Graph ,Main Eigenvalue ,Cyclic Group ,Prime Divisor
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آدرس
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University Of Kashan, Faculty Of Mathematical Sciences, Department Of Pure Mathematics, ایران, University Of Kashan, Faculty Of Mathematical Sciences, Department Of Pure Mathematics, ایران
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پست الکترونیکی
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gh.fathtabar@gmail.com
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Authors
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