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Edge-determining
sets and determining index
Sally Cockburn and Sean McAvoy |
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Vol. 17 (2024), No. 1, 85–106
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Abstract |
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A graph automorphism is a bijective mapping of the vertices that preserves adjacent vertices. A vertex-determining set of a graph is a set of vertices such that the only automorphism that fixes those vertices is the identity. The size of a smallest such set is called the determining number, denoted by . The determining number is a parameter of the graph capturing its level of symmetry. We introduce the related concept of an edge-determining set and determining index, . We prove that when and show both bounds are sharp for infinite families of graphs. Further, we investigate properties of these new concepts, as well as provide the determining index for several families of graphs, including hypercubes. |
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Keywords
determining number, distinguishing index, hypercubes
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Mathematical Subject Classification
Primary: 05C25
Secondary: 05C70
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Milestones
Received: 29 July 2022
Revised: 30 December 2022
Accepted: 30 December 2022
Published: 15 March 2024
Communicated by Anant Godbole
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Authors |
| Sally Cockburn | |
| Mathematics and Statistics
Department Hamilton College Clinton, NY United States |
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| Sean McAvoy | |
| Department of Statistics University of California Berkeley, CA United States |
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| © 2024 MSP (Mathematical Sciences Publishers). |
