On the betanumber of forests with isomorphic components
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2018Suggested citation
Ichishima, R.;
López Masip, SusanaClara;
Muntaner Batle, F. A.;
Oshima, A.;
.
(2018)
.
On the betanumber of forests with isomorphic components.
Discussiones Mathematicae Graph Theory, 2018, vol. 38, num. 3, p. 683701.
https://doi.org/10.7151/dmgt.2033.
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The betanumber, 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 betanumber is called the strong betanumber 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) betanumber of forests whose components are isomorphic to either paths or stars.
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Discussiones Mathematicae Graph Theory, 2018, vol. 38, num. 3, p. 683701European research projects
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Except where otherwise noted, this item's license is described as ccbyncnd (c) De Gruyter Open, 2018
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