A note on 4-regular distance magic graphs
Petr Kovář, Dalibor Fronček, Tereza Kovářová · 2012
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 thatu∈N(v) f (u )= k for all v ∈ V , where N(v) is the set of all vertices adjacent to v. The constant k is the magic constant of f and any graph which admits a distance magic labeling is a distance magic graph .I n 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 =2 t for every integer t ≥ 6.