K. Sankar and V. Sivakumaran. Existence of Distance Magic Graph for Every Magic Constant. Dynamic Systems and Applications 30 (2021) No.8, 1335 – 1345

https://doi.org/10.46719/dsa20213088

ABSTRACT.
Assume G = (V, E) is an n ordered plain graph.  The distance magic labeling of G is invertible function f : V(G) → {1, 2, …, n} with a quality that a positive integer k exists in order that, for u ∈ N(v) , ∑ f(u) = k for every v ∈ V(G), here N(v) is a group of complete vertices of V(G) that are near to v, called open neighborhood of the vertex v. Here, existence of simple or simple graph with an isolated self loop vertex as a distance magic graph for every magic invariable k  ≥ 2 is proved.

Keywords: Distance Magic Graph, Distance Magic Constant.
Mathematics Subject Classification: 05C78.