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Currently displaying 1 – 2 of 2

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Labeling the vertex amalgamation of graphs

Ramon M. Figueroa-Centeno; Rikio Ichishima; Francesc A. Muntaner-Batle — 2003

Discussiones Mathematicae Graph Theory

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 $f : V (G) \to Z_{q}$ 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 $f : V (G) \to Z_{q + 1}$ such that each edge uv of G is labeled f(u) + f(v) mod q and the...

A magical approach to some labeling conjectures

Ramon M. Figueroa-Centeno; Rikio Ichishima; Francesc A. Muntaner-Batle; Akito Oshima — 2011

Discussiones Mathematicae Graph Theory

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...

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