- Tytuł:
- Nowhere-zero modular edge-graceful graphs
- Autorzy:
-
Jones, Ryan
Zhang, Ping - Powiązania:
- https://bibliotekanauki.pl/articles/743248.pdf
- Data publikacji:
- 2012
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
modular edge-graceful labelings and graphs
nowhere-zero labelings
modular edge-gracefulness - Opis:
- 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 $f'(u) = ∑_{v ∈ N(u)} f(uv)$, 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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2012, 32, 3; 487-505
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł