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Structural
properties of group power digraphs
Ben Grant, Robert Ireland, E. Koenig and Adam Wood |
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Vol. 16 (2023), No. 5, 809–832
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Abstract |
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We study group power digraphs , where is a finite group and is a positive integer. A group power digraph is a directed graph derived from the power function on a finite group . We present results on various properties of these power digraphs, including indegree of vertices, structure of components, existence of cycles, and a certain type of symmetry. Arbitrary finite groups are discussed briefly, but the focus of this paper is on three families of finite groups: cyclic, dihedral, and symmetric groups. In each case, properties specific to the family of groups are presented. |
Keywords
directed graph, finite group, power digraph, $m$-symmetry
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Mathematical Subject Classification
Primary: 05C20, 05C25
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Milestones
Received: 26 May 2022
Revised: 8 December 2022
Accepted: 9 December 2022
Published: 9 December 2023
Communicated by Ronald Gould
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Authors |
| Ben Grant | |
| Mathematics, Statistics, and
Computer Science Department St. Olaf College Northfield, MN United States |
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| Robert Ireland | |
| Mathematics, Statistics, and
Computer Science Department St. Olaf College Northfield, MN United States |
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| E. Koenig | |
| Mathematics, Statistics, and
Computer Science Department St. Olaf College Northfield, MN United States |
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| Adam Wood | |
| Mathematics, Statistics and Computer
Science Department St. Olaf College Northfield, MN United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
