Digraphs from endomorphisms of finite cyclic groups (Q2839733)
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scientific article; zbMATH DE number 6187633
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Digraphs from endomorphisms of finite cyclic groups |
scientific article; zbMATH DE number 6187633 |
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12 July 2013
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cyclic group
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digraph
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adjacency matrix
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automorphism group
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math.CO
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Digraphs from endomorphisms of finite cyclic groups (English)
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Let \(H=\langle x\rangle\) be a finite cyclic group with \(n\) elements, \(n>1\). Every endomorphism of \(H\) has a unique form \(f: x\mapsto x^k\), \(1\leq k\leq n\). We can consider the digraph \(G(n,k)\) that has the elements of \(H\) as vertices and a directed edge \((a,b)\) if \(f(a)=b\).NEWLINENEWLINEThe author studies many properties of this digraph, including its adjacency matrix and automorphism group.
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