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dc.contributor.authorIchishima, R.
dc.contributor.authorLópez Masip, Susana Clara
dc.contributor.authorMuntaner Batle, Francesc Antoni
dc.contributor.authorOshima, Akito
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationIchishima, 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.description.abstractThe 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.extent19 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshGraph theory
dc.subject.otherstrong beta-number
dc.subject.othergraceful labeling
dc.subject.otherSkolem sequence
dc.subject.otherhooked Skolem sequence
dc.titleOn the beta-number of forests with isomorphic components
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
local.citation.authorIchishima, R.; López, S.C.; Muntaner-Batle, F.A.; Oshima, A.
local.citation.publicationNameDiscussiones mathematicae. Graph theory

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