## Abstract

Let G = (V,E) be a graph on n vertices. A bijection f: V → {1, 2,..., n} is called a distance magic labeling of G if there exists an integer k such that ∑ _{u∈N(υ)} f(u) = k for all υ ∈ V, where N(υ) is the set of all vertices adjacent to υ. The constant k is the magic constant of f and any graph which admits a distance magic labeling is a distance magic graph. In this paper we solve some of the problems posted in a recent survey paper on distance magic graph labelings by Arumugam et al. We classify all orders n for which a 4-regular distance magic graph exists and by this we also show that there exists a distance magic graph with k = 2t for every integer t ≥ 6.

Original language | English (US) |
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Pages (from-to) | 127-132 |

Number of pages | 6 |

Journal | Australasian Journal of Combinatorics |

Volume | 54 |

Issue number | 2 |

State | Published - Oct 4 2012 |