Nowhere-zero modular edge-graceful graphs

Ryan Jones ; Ping Zhang

Discussiones Mathematicae Graph Theory, Tome 32 (2012), p. 487-505 / Harvested from The Polish Digital Mathematics Library

Résumé

For a connected graph G of order n ≥ 3, let f: E(G) → ℤₙ be an edge labeling of G. The vertex labeling f’: V(G) → ℤₙ induced by f is defined as $f^{\prime }(u) = ∑_{v ∈ N(u)} f(uv)$, where the sum is computed in ℤₙ. If f’ is one-to-one, then f is called a modular edge-graceful labeling and G is a modular edge-graceful graph. A modular edge-graceful labeling f of G is nowhere-zero if f(e) ≠ 0 for all e ∈ E(G) and in this case, G is a nowhere-zero modular edge-graceful graph. It is shown that a connected graph G of order n ≥ 3 is nowhere-zero modular edge-graceful if and only if n ≢ 2 mod 4, G ≠ K₃ and G is not a star of even order. For a connected graph G of order n ≥ 3, the smallest integer k ≥ n for which there exists an edge labeling f: E(G) → ℤₖ - 0 such that the induced vertex labeling f’ is one-to-one is referred to as the nowhere-zero modular edge-gracefulness of G and this number is determined for every connected graph of order at least 3.

Détail

Publié le : 2012-01-01

Zbl 1257.05151

EUDML-ID : urn:eudml:doc:271066

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