- Tytuł:
- Labeling the vertex amalgamation of graphs
- Autorzy:
-
Figueroa-Centeno, Ramon
Ichishima, Rikio
Muntaner-Batle, Francesc - Powiązania:
- https://bibliotekanauki.pl/articles/743389.pdf
- Data publikacji:
- 2003
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
felicitous labellings
graceful labellings
harmonious labellings. - Opis:
- A graph G of size q is graceful if there exists an injective function f:V(G)→ {0,1,...,q} such that each edge uv of G is labeled |f(u)-f(v)| and the resulting edge labels are distinct. Also, a (p,q) graph G with q ≥ p is harmonious if there exists an injective function $f:V(G) → Z_q$ such that each edge uv of G is labeled f(u) + f(v) mod q and the resulting edge labels are distinct, whereas G is felicitous if there exists an injective function $f: V(G) → Z_{q+1}$ such that each edge uv of G is labeled f(u) + f(v) mod q and the resulting edge labels are distinct. In this paper, we present several results involving the vertex amalgamation of graceful, felicitous and harmonious graphs. Further, we partially solve an open problem of Lee et al., that is, for which m and n the vertex amalgamation of n copies of the cycle Cₘ at a fixed vertex v ∈ V(Cₘ), Amal(Cₘ,v,n), is felicitous? Moreover, we provide some progress towards solving the conjecture of Koh et al., which states that the graph Amal(Cₘ,v,n) is graceful if and only if mn ≡ 0 or 3 mod 4. Finally, we propose two conjectures.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2003, 23, 1; 129-139
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł