dc.contributor.author Ichishima, R. dc.contributor.author López Masip, Susana Clara dc.contributor.author Muntaner Batle, Francesc Antoni dc.contributor.author Oshima, Akito dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2018-10-02T10:40:47Z dc.date.available 2018-10-02T10:40:47Z dc.date.issued 2018 dc.identifier.citation Ichishima, R., López, S.C., Muntaner-Batle, F.A., Oshima, A. On the beta-number of forests with isomorphic components. "Discussiones mathematicae. Graph theory", 2018, vol. 38, núm. 3, p. 683-701. dc.identifier.issn 1234-3099 dc.identifier.uri http://hdl.handle.net/2117/121742 dc.description.abstract The beta-number, ß (G), of a graph G is defined to be either the smallest positive integer n for which there exists an injective function f : V (G) ¿ {0, 1, . . . , n} such that each uv ¿ E (G) is labeled |f (u) - f (v)| and the resulting set of edge labels is {c, c + 1, . . . , c + |E (G)| - 1} for some positive integer c or +8 if there exists no such integer n. If c = 1, then the resulting beta-number is called the strong beta-number of G and is denoted by ßs (G). In this paper, we show that if G is a bipartite graph and m is odd, then ß (mG) = mß (G) + m - 1. This leads us to conclude that ß (mG) = m |V (G)| -1 if G has the additional property that G is a graceful nontrivial tree. In addition to these, we examine the (strong) beta-number of forests whose components are isomorphic to either paths or stars. dc.format.extent 19 p. dc.language.iso eng dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística dc.subject.lcsh Graph theory dc.subject.other beta-number dc.subject.other strong beta-number dc.subject.other graceful labeling dc.subject.other Skolem sequence dc.subject.other hooked Skolem sequence dc.title On the beta-number of forests with isomorphic components dc.type Article dc.subject.lemac Grafs, Teoria de dc.contributor.group Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions dc.identifier.doi 10.7151/dmgt.2033 dc.rights.access Open Access local.identifier.drac 23290370 dc.description.version Postprint (author's final draft) local.citation.author Ichishima, R.; López, S.C.; Muntaner-Batle, F.A.; Oshima, A. local.citation.publicationName Discussiones mathematicae. Graph theory local.citation.volume 38 local.citation.number 3 local.citation.startingPage 683 local.citation.endingPage 701
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