- Tytuł:
- On {a, b}-Edge-Weightings of Bipartite Graphs with Odd a, b
- Autorzy:
-
Bensmail, Julien
Inerney, Fionn Mc
Lyngsie, Kasper Szabo - Powiązania:
- https://bibliotekanauki.pl/articles/32361745.pdf
- Data publikacji:
- 2022-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
neighbour-sum-distinguishing edge-weightings
bipartite graphs
odd weights
1-2-3 Conjecture - Opis:
- For any S ⊂ ℤ we say that a graph G has the S-property if there exists an S-edge-weighting w : E(G) → S such that for any pair of adjacent vertices u, v we have ∑e∈E(v) w(e) ≠ ∑e∈E(u) w(e), where E(v) and E(u) are the sets of edges incident to v and u, respectively. This work focuses on {a, a+2}-edge-weightings where a ∈ ℤ is odd. We show that a 2-connected bipartite graph has the {a, a+2}-property if and only if it is not a so-called odd multi-cactus. In the case of trees, we show that only one case is pathological. That is, we show that all trees have the {a, a+2}-property for odd a ≠ −1, while there is an easy characterization of trees without the {−1, 1}-property.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2022, 42, 1; 159-185
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł