Caterpillars have antimagic orientations
An antimagic labeling of a directed graph D with m arcs is a bijection from the set of arcs of D to {1, . . . , m} such that all oriented vertex sums of vertices in D are pairwise distinct, where the oriented vertex sum of a vertex u is the sum of labels of all arcs entering u minus the sum of label...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| 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:2117/128051 |
| Acceso en línea: | https://hdl.handle.net/2117/128051 https://dx.doi.org/10.2478/auom-2018-0039 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory Caterpillar Antimagic labeling Antimagic orientation Grafs, Teoria de Classificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Sumario: | An antimagic labeling of a directed graph D with m arcs is a bijection from the set of arcs of D to {1, . . . , m} such that all oriented vertex sums of vertices in D are pairwise distinct, where the oriented vertex sum of a vertex u is the sum of labels of all arcs entering u minus the sum of labels of all arcs leaving u. Hefetz, Mütze, and Schwartz [3] conjectured that every connected graph admits an antimagic orientation, where an antimagic orientation of a graph G is an orientation of G which has an antimagic labeling. We use a constructive technique to prove that caterpillars, a well-known subclass of trees, have antimagic orientations. |
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