Labeling the vertex amalgamation of graphs
Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 129-139
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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.
Keywords:
felicitous labellings, graceful labellings, harmonious labellings.
@article{DMGT_2003_23_1_a8,
author = {Figueroa-Centeno, Ramon and Ichishima, Rikio and Muntaner-Batle, Francesc},
title = {Labeling the vertex amalgamation of graphs},
journal = {Discussiones Mathematicae. Graph Theory},
pages = {129--139},
publisher = {mathdoc},
volume = {23},
number = {1},
year = {2003},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGT_2003_23_1_a8/}
}
TY - JOUR AU - Figueroa-Centeno, Ramon AU - Ichishima, Rikio AU - Muntaner-Batle, Francesc TI - Labeling the vertex amalgamation of graphs JO - Discussiones Mathematicae. Graph Theory PY - 2003 SP - 129 EP - 139 VL - 23 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMGT_2003_23_1_a8/ LA - en ID - DMGT_2003_23_1_a8 ER -
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Figueroa-Centeno, Ramon; Ichishima, Rikio; Muntaner-Batle, Francesc. Labeling the vertex amalgamation of graphs. Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 129-139. http://geodesic.mathdoc.fr/item/DMGT_2003_23_1_a8/