Let G be a graph of order n and let S be a set of positive integers with |S| = n. Then G is said to be S-magic if there exists a bijection ϕ : V (G) → S satisfying ∑x∈N(u) ϕ(x) = k (a constant) for every u ∈ V (G). Let α(S) = max{s : s ∈ S}. Let i(G) = min α(S), where the minimum is taken over all sets S for which the graph G admits an S-magic labeling. Then i(G) − n is called the distance magic index of the graph G. In this paper we determine the distance magic index of trees and complete bipartite graphs.
@article{bwmeta1.element.doi-10_7151_dmgt_1998,
author = {Aloysius Godinho and Tarkeshwar Singh and S. Arumugam},
title = {The Distance Magic Index of a Graph},
journal = {Discussiones Mathematicae Graph Theory},
volume = {38},
year = {2018},
pages = {135-142},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1998}
}
Aloysius Godinho; Tarkeshwar Singh; S. Arumugam. The Distance Magic Index of a Graph. Discussiones Mathematicae Graph Theory, Tome 38 (2018) pp. 135-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1998/