- Tytuł:
- On the Beta-Number of Forests with Isomorphic Components
- Autorzy:
-
Ichishima, Rikio
López, Susana-Clara
Muntaner-Batle, Francesc Antoni
Oshima, Akito - Powiązania:
- https://bibliotekanauki.pl/articles/31342282.pdf
- Data publikacji:
- 2018-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
beta-number
strong beta-number
graceful labeling
Skolem sequence
hooked Skolem sequence - Opis:
- The 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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2018, 38, 3; 683-701
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł