Geodesic
Labeling the vertex amalgamation of graphs
Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 129-139

Voir la notice de l'article provenant de la source Library of Science

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  - 
%0 Journal Article
%A Figueroa-Centeno, Ramon
%A Ichishima, Rikio
%A Muntaner-Batle, Francesc
%T Labeling the vertex amalgamation of graphs
%J Discussiones Mathematicae. Graph Theory
%D 2003
%P 129-139
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2003_23_1_a8/
%G en
%F DMGT_2003_23_1_a8
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/