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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Detalles Bibliográficos
Autor: Lozano Boixadors, Antoni|||0000-0002-3633-063X
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
Descripción
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.