### Abstract

A handicap distance antimagic labeling of a graph G = (V,E) with n vertices is a bijection f: V → {1, 2, . . ., ng with the property that f(x_{i}) = i, the weight w(x_{i}) is the sum of labels of all neighbors of x_{i}, and the sequence of the weights w(x_{1}),w(x_{2}), . . ., w(x_{n}) forms an increasing arithmetic progression. A graph G is a handicap distance antimagic graph if it allows a handicap distance antimagic labeling. We construct r-regular handicap distance antimagic graphs of order n ≡ 0 (mod 8) for all feasible values of r.

Original language | English (US) |
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Pages (from-to) | 208-218 |

Number of pages | 11 |

Journal | Electronic Journal of Graph Theory and Applications |

Volume | 6 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2018 |

### Keywords

- Graph labeling
- Handicap labeling
- Regular graphs
- Tournament scheduling

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## Cite this

Froncek, D., & Shepanik, A. L. (2018). Regular handicap graphs of order n ≡ 0 (mod 8).

*Electronic Journal of Graph Theory and Applications*,*6*(2), 208-218. https://doi.org/10.5614/ejgta.2018.6.2.1