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dc.contributor.authorIchishima, R.
dc.contributor.authorLópez Masip, Susana-Clara
dc.contributor.authorMuntaner Batle, F. A.
dc.contributor.authorOshima, A.
dc.description.abstractThe beta-number, β (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 +∞ 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 βs (G). In this paper, we show that if G is a bipartite graph and m is odd, then β (mG) ≤ mβ (G) + m − 1. This leads us to conclude that β (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.publisherDe Gruyter Open
dc.relation.isformatofReproducció del document publicat a
dc.relation.ispartofDiscussiones Mathematicae Graph Theory, 2018, vol. 38, num. 3, p. 683-701
dc.rightscc-by-nc-nd (c) De Gruyter Open, 2018
dc.subjectStrong beta-number
dc.subjectGraceful labeling
dc.subjectSkolem sequence
dc.subjectHooked Skolem sequence
dc.titleOn the beta-number of forests with isomorphic components

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cc-by-nc-nd (c) De Gruyter Open, 2018
Except where otherwise noted, this item's license is described as cc-by-nc-nd (c) De Gruyter Open, 2018