Antimagic labellings of (k, 2)-bipartite biregular graphs
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915193302286336 |
|---|---|
| author | Beaudoire, Grégoire Bentz, Cédric Picouleau, Christophe |
| author_facet | Beaudoire, Grégoire Bentz, Cédric Picouleau, Christophe |
| contents | An antimagic labelling of a graph is a bijection from the set of edges to $\{1, 2, \ldots , m\}$, such that all vertex-sums are pairwise distinct, where the vertex-sum of a vertex is the sum of labels on the edges incident to it. We say a graph is antimagic if it has an antimagic labelling. In 2023, it has been proven that connected $(k, l)$-bipartite graphs are antimagic if $k \geq l + 2$ and one of k or l is odd. In this paper, we extend this result to connected $(k, 2)$-bipartite biregular graphs for $k \geq 4$ even, and to $(k, 2)$-bipartite biregular graphs for $k \geq 3$ odd. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11931 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Antimagic labellings of (k, 2)-bipartite biregular graphs Beaudoire, Grégoire Bentz, Cédric Picouleau, Christophe Combinatorics An antimagic labelling of a graph is a bijection from the set of edges to $\{1, 2, \ldots , m\}$, such that all vertex-sums are pairwise distinct, where the vertex-sum of a vertex is the sum of labels on the edges incident to it. We say a graph is antimagic if it has an antimagic labelling. In 2023, it has been proven that connected $(k, l)$-bipartite graphs are antimagic if $k \geq l + 2$ and one of k or l is odd. In this paper, we extend this result to connected $(k, 2)$-bipartite biregular graphs for $k \geq 4$ even, and to $(k, 2)$-bipartite biregular graphs for $k \geq 3$ odd. |
| title | Antimagic labellings of (k, 2)-bipartite biregular graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.11931 |