Strong vertex-magic and edge-magic labelings of 2-regular graphs of odd order using Kotzig completion
| Autor: | Dan McQuillan, James M. McQuillan |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Edge-graceful labeling Magic (programming) 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 01 natural sciences Graph Theoretical Computer Science Vertex (geometry) Combinatorics 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Mathematics |
| Zdroj: | Discrete Mathematics. 341:194-202 |
| ISSN: | 0012-365X |
| Popis: | Let G be a 2-regular graph with 2 m + 1 vertices and assume that G has a strong vertex-magic total labeling. It is shown that the four graphs G ∪ 2 m C 3 , G ∪ ( 2 m + 2 ) C 3 , G ∪ m C 8 and G ∪ ( m + 1 ) C 8 also have a strong vertex-magic total labeling. These theorems follow from a new use of carefully prescribed Kotzig arrays. To illustrate the power of this technique, we show how just three of these arrays, combined with known labelings for smaller 2-regular graphs, immediately provide strong vertex-magic total labelings for 68 different 2-regular graphs of order 49. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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