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Labeling the vertex amalgamation of graphs

100%

Figueroa-Centeno R., Ichishima R., Muntaner-Batle F.

Discussiones Mathematicae Graph Theory

2003

tom 23

nr 1

129-139

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.

A magical approach to some labeling conjectures

100%

Figueroa-Centeno R., Ichishima R., Muntaner-Batle F., Oshima A.

Discussiones Mathematicae Graph Theory

2011

tom 31

nr 1

79-113

In this paper, a complete characterization of the (super) edge-magic linear forests with two components is provided. In the process of establishing this characterization, the super edge-magic, harmonious, sequential and felicitous properties of certain 2-regular graphs are investigated, and several results on super edge-magic and felicitous labelings of unions of cycles and paths are presented. These labelings resolve one conjecture on harmonious graphs as a corollary, and make headway towards the resolution of others. They also provide the basis for some new conjectures (and a weaker form of an old one) on labelings of 2-regular graphs.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Figueroa-Centeno R.

2 Ichishima R.

2 Muntaner-Batle F.

1 Oshima A.

1 2011

1 2003

Wyniki wyszukiwania

Labeling the vertex amalgamation of graphs

A magical approach to some labeling conjectures