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Antimagic labelings of caterpillars
dc.contributor.author | Lozano Boixadors, Antoni |
dc.contributor.author | Mora Giné, Mercè |
dc.contributor.author | Seara Ojea, Carlos |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Ciències de la Computació |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2018-12-13T12:55:58Z |
dc.date.available | 2020-12-01T02:01:58Z |
dc.date.issued | 2019-04-15 |
dc.identifier.citation | Lozano, A., Mora, M., Seara, C. Antimagic labelings of caterpillars. "Applied mathematics and computation", 15 Abril 2019, vol. 347, p. 734-740. |
dc.identifier.issn | 0096-3003 |
dc.identifier.other | https://arxiv.org/abs/1708.00624 |
dc.identifier.uri | http://hdl.handle.net/2117/125781 |
dc.description.abstract | A 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.extent | 7 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat |
dc.subject.lcsh | Algorithms |
dc.subject.lcsh | Graph theory |
dc.subject.lcsh | Trees (Graph theory) |
dc.subject.other | Antimagic graphs |
dc.subject.other | Labelings |
dc.title | Antimagic labelings of caterpillars |
dc.type | Article |
dc.subject.lemac | Algorismes |
dc.subject.lemac | Grafs, Teoria de |
dc.subject.lemac | Arbres (Teoria de grafs) |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.contributor.group | Universitat Politècnica de Catalunya. DCG - Discrete and Combinatorial Geometry |
dc.contributor.group | Universitat Politècnica de Catalunya. CGA - Computational Geometry and Applications |
dc.identifier.doi | 10.1016/j.amc.2018.11.043 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | https://www.sciencedirect.com/science/article/abs/pii/S0096300318310178 |
dc.rights.access | Open Access |
local.identifier.drac | 23552785 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/648276/EU/A Unified Theory of Algorithmic Relaxations/AUTAR |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT |
dc.relation.projectid | info:eu-repo/grantAgreement/AGAUR/2017SGR1640 |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2015-63791-R/ES/GRAFOS Y GEOMETRIA: INTERACCIONES Y APLICACIONES/ |
local.citation.author | Lozano, A.; Mora, M.; Seara, C. |
local.citation.publicationName | Applied mathematics and computation |
local.citation.volume | 347 |
local.citation.startingPage | 734 |
local.citation.endingPage | 740 |
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