Caterpillars are antimagic
An antimagic labeling of a graph G is a bijection from the set of edges E(G) to {1,2,…,|E(G)|}, such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to the edges incident to u. A graph is called antimagic when it has an antimagic labelin...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/340688 |
| Acceso en línea: | https://hdl.handle.net/2117/340688 https://dx.doi.org/10.1007/s00009-020-01688-z |
| Access Level: | acceso abierto |
| Palabra clave: | Algorithms Graph theory Antimagic Graphs Caterpillars Algorismes Grafs, Teoria de Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Sumario: | An antimagic labeling of a graph G is a bijection from the set of edges E(G) to {1,2,…,|E(G)|}, such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to the edges incident to u. A graph is called antimagic when it has an antimagic labeling. Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic and the conjecture remains open even for trees. Here, we prove that caterpillars are antimagic by means of an O(nlogn) algorithm. |
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