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Title:
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Trees whose even-degree vertices induce a path are antimagic
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Author:
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Lozano Bojados, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos; Tey Carrera, Joaquín
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Ciències de la Computació; Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions; Universitat Politècnica de Catalunya. DCG - Discrete and Combinatorial Geometry; Universitat Politècnica de Catalunya. CGA -Computational Geometry and Applications |
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Abstract:
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An antimagic labeling of a connected 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 v is the sum of the labels assigned to edges incident to v. A graph is called antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic; however, the conjecture remains open, even for trees. In this note we prove that trees whose vertices of even degree induce a path are antimagic, extending a result given by Liang, Wong, and Zhu [Discrete Math. 331 (2014) 9–14]. |
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Subject(s):
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-Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat
-Graph theory
-Algorithms
-Antimagic labeling
-Graph
-Tree
-Grafs, Teoria de
-Algorismes |
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Rights:
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Document type:
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Article - Draft
Report |
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