Show simple item record

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.date.accessioned2018-10-02T10:40:47Z
dc.date.available2018-10-02T10:40:47Z
dc.date.issued2018
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.identifier.issn1234-3099
dc.identifier.urihttp://hdl.handle.net/2117/121742
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.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshGraph theory
dc.subject.otherbeta-number
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.typeArticle
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.identifier.doi10.7151/dmgt.2033
dc.rights.accessOpen Access
local.identifier.drac23290370
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
local.citation.volume38
local.citation.number3
local.citation.startingPage683
local.citation.endingPage701


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder