Geodesic
The Distance Magic Index of a Graph
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 135-142

Voir la notice de l'article provenant de la source Library of Science

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 Σ_ 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.
Keywords: distance magic labeling, distance magic index, S -magic graph, S -magic labeling 
@article{DMGT_2018_38_1_a10,
     author = {Godinho, Aloysius and Singh, Tarkeshwar and Arumugam, S.},
     title = {The {Distance} {Magic} {Index} of a {Graph}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {135--142},
     publisher = {mathdoc},
     volume = {38},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a10/}
}
TY  - JOUR
AU  - Godinho, Aloysius
AU  - Singh, Tarkeshwar
AU  - Arumugam, S.
TI  - The Distance Magic Index of a Graph
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2018
SP  - 135
EP  - 142
VL  - 38
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a10/
LA  - en
ID  - DMGT_2018_38_1_a10
ER  - 
%0 Journal Article
%A Godinho, Aloysius
%A Singh, Tarkeshwar
%A Arumugam, S.
%T The Distance Magic Index of a Graph
%J Discussiones Mathematicae. Graph Theory
%D 2018
%P 135-142
%V 38
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a10/
%G en
%F DMGT_2018_38_1_a10
Godinho, Aloysius; Singh, Tarkeshwar; Arumugam, S. The Distance Magic Index of a Graph. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 135-142. http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a10/