### Resumen

A graph G=(V,E) is weighted- k-antimagic if for each w:V→R, there is an injective function f:E→{1,…,|E|+k} such that the following sums are all distinct: for each vertex u, ∑_{v:uv∈E}f(uv)+w(u). When such a function f exists, it is called a (w,k)-antimagic labeling of G. A connected graph G is antimagic if it has a (w_{0},0)-antimagic labeling, for w_{0}(u)=0, for each u∈V. In this work, we prove that all the complete bipartite graphs K_{p,q}, are weighted-0-antimagic when 2≤p≤q and q≥3. Moreover, an algorithm is proposed that computes in polynomial time a (w,0)-antimagic labeling of the graph. Our result implies that if H is a complete partite graph, with H≠K_{1,q}, K_{2,2}, then any connected graph G containing H as a spanning subgraph is antimagic.

Idioma original | English |
---|---|

Páginas (desde-hasta) | 194-201 |

Número de páginas | 8 |

Publicación | Discrete Applied Mathematics |

Volumen | 245 |

DOI | |

Estado | Published - 20 ago 2018 |

### Huella dactilar

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Citar esto

*Discrete Applied Mathematics*,

*245*, 194-201. https://doi.org/10.1016/j.dam.2017.05.006

}

*Discrete Applied Mathematics*, vol. 245, pp. 194-201. https://doi.org/10.1016/j.dam.2017.05.006

**Weighted antimagic labeling.** / Matamala, Martín; Zamora, José.

Resultado de la investigación: Article

TY - JOUR

T1 - Weighted antimagic labeling

AU - Matamala, Martín

AU - Zamora, José

PY - 2018/8/20

Y1 - 2018/8/20

N2 - A graph G=(V,E) is weighted- k-antimagic if for each w:V→R, there is an injective function f:E→{1,…,|E|+k} such that the following sums are all distinct: for each vertex u, ∑v:uv∈Ef(uv)+w(u). When such a function f exists, it is called a (w,k)-antimagic labeling of G. A connected graph G is antimagic if it has a (w0,0)-antimagic labeling, for w0(u)=0, for each u∈V. In this work, we prove that all the complete bipartite graphs Kp,q, are weighted-0-antimagic when 2≤p≤q and q≥3. Moreover, an algorithm is proposed that computes in polynomial time a (w,0)-antimagic labeling of the graph. Our result implies that if H is a complete partite graph, with H≠K1,q, K2,2, then any connected graph G containing H as a spanning subgraph is antimagic.

AB - A graph G=(V,E) is weighted- k-antimagic if for each w:V→R, there is an injective function f:E→{1,…,|E|+k} such that the following sums are all distinct: for each vertex u, ∑v:uv∈Ef(uv)+w(u). When such a function f exists, it is called a (w,k)-antimagic labeling of G. A connected graph G is antimagic if it has a (w0,0)-antimagic labeling, for w0(u)=0, for each u∈V. In this work, we prove that all the complete bipartite graphs Kp,q, are weighted-0-antimagic when 2≤p≤q and q≥3. Moreover, an algorithm is proposed that computes in polynomial time a (w,0)-antimagic labeling of the graph. Our result implies that if H is a complete partite graph, with H≠K1,q, K2,2, then any connected graph G containing H as a spanning subgraph is antimagic.

KW - Antimagic labeling

KW - Complete bipartite graph

KW - Graph labeling

KW - Weighted antimagic labeling

UR - http://www.scopus.com/inward/record.url?scp=85020419525&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2017.05.006

DO - 10.1016/j.dam.2017.05.006

M3 - Article

AN - SCOPUS:85020419525

VL - 245

SP - 194

EP - 201

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -