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...

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Detalles Bibliográficos
Autores: Lozano Boixadors, Antoni|||0000-0002-3633-063X, Mora Giné, Mercè|||0000-0001-6923-0320, Seara Ojea, Carlos|||0000-0002-0095-1725, Tey Carrera, Joaquín
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
Descripción
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.