### Resumen

Hartsfield and Ringel in 1990 conjectured that any connected graph with q≥2 edges has an edge labeling f with labels in the set {1,…,q}, such that for every two distinct vertices u and v, f^{u}≠f^{v}, where f^{v}=∑_{e∈E(v)}f(e), and E(v) is the set of edges of the graph incident to vertex v. We say that a graph G=(V,E), with q edges, is universal antimagic, if for every set B of q positive numbers there is a bijection f:E→B such that f^{u}≠f^{v}, for any two distinct vertices u and v. It is weighted universal antimagic if for any vertex weight function w and every set B of q positive numbers there is a bijection f:E→B such that w(u)+f^{u}≠w(v)+f^{v}, for any two distinct vertices u and v. In this work we prove that paths, cycles, and graphs whose connected components are cycles or paths of odd lengths are universal antimagic. We also prove that a split graph and any graph containing a complete bipartite graph as a spanning subgraph is universal antimagic. Surprisingly, we are also able to prove that any graph containing a complete bipartite graph K_{n,m} with n,m≥3 as a spanning subgraph is weighted universal antimagic. From all the results we can derive effective methods to construct the labelings.

Idioma original | Inglés |
---|---|

Páginas (desde-hasta) | 246-251 |

Número de páginas | 6 |

Publicación | Discrete Applied Mathematics |

Volumen | 281 |

DOI | |

Estado | En prensa - 1 ene 2019 |

### Áreas temáticas de ASJC Scopus

- Matemáticas discretas y combinatorias
- Matemáticas aplicadas

## Huella Profundice en los temas de investigación de 'Graphs admitting antimagic labeling for arbitrary sets of positive numbers'. En conjunto forman una huella única.

## Citar esto

*Discrete Applied Mathematics*,

*281*, 246-251. https://doi.org/10.1016/j.dam.2019.10.011