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dc.contributor.authorLozano Boixadors, Antoni
dc.contributor.authorMora Giné, Mercè
dc.contributor.authorSeara Ojea, Carlos
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Ciències de la Computació
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2018-12-13T12:55:58Z
dc.date.available2020-12-01T02:01:58Z
dc.date.issued2019-04-15
dc.identifier.citationLozano, A., Mora, M., Seara, C. Antimagic labelings of caterpillars. "Applied mathematics and computation", 15 Abril 2019, vol. 347, p. 734-740.
dc.identifier.issn0096-3003
dc.identifier.otherhttps://arxiv.org/abs/1708.00624
dc.identifier.urihttp://hdl.handle.net/2117/125781
dc.description.abstractA k-antimagic labeling of a graph G is an injection from E(G) to {1,2, ..., |E(G)|+k} such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to edges incident to u. We call a graph k-antimagic when it has a k-antimagic labeling, and antimagic when it is 0-antimagic. Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic, but the conjecture is still open even for trees. Here we study k-antimagic labelings of caterpillars. We use algorithmic and constructive techniques, instead of the standard Combinatorial NullStellenSatz method, to prove our results: (i) any caterpillar of order n is (⌊(n−1)/2⌋−2)-antimagic; (ii) any caterpillar with a spine of order s with either at least ⌊(3s+1)/2⌋ leaves or ⌊(s−1)/2⌋ consecutive vertices of degree at most 2 at one end of a longest path, is antimagic; and (iii) if p is a prime number, any caterpillar with a spine of order p, p−1 or p−2 is 1-antimagic.
dc.format.extent7 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat
dc.subject.lcshAlgorithms
dc.subject.lcshGraph theory
dc.subject.lcshTrees (Graph theory)
dc.subject.otherAntimagic graphs
dc.subject.otherLabelings
dc.titleAntimagic labelings of caterpillars
dc.typeArticle
dc.subject.lemacAlgorismes
dc.subject.lemacGrafs, Teoria de
dc.subject.lemacArbres (Teoria de grafs)
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.contributor.groupUniversitat Politècnica de Catalunya. DCG - Discrete and Combinatorial Geometry
dc.contributor.groupUniversitat Politècnica de Catalunya. CGA - Computational Geometry and Applications
dc.identifier.doi10.1016/j.amc.2018.11.043
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/abs/pii/S0096300318310178
dc.rights.accessOpen Access
local.identifier.drac23552785
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/648276/EU/A Unified Theory of Algorithmic Relaxations/AUTAR
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT
dc.relation.projectidinfo:eu-repo/grantAgreement/AGAUR/2017SGR1640
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO//MTM2015-63791-R/ES/GRAFOS Y GEOMETRIA: INTERACCIONES Y APLICACIONES/
local.citation.authorLozano, A.; Mora, M.; Seara, C.
local.citation.publicationNameApplied mathematics and computation
local.citation.volume347
local.citation.startingPage734
local.citation.endingPage740


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