# The Distance Magic Index of a Graph

• Volume: 38, Issue: 1, page 135-142
• ISSN: 2083-5892

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## Abstract

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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.

## How to cite

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Aloysius Godinho, Tarkeshwar Singh, and S. Arumugam. "The Distance Magic Index of a Graph." Discussiones Mathematicae Graph Theory 38.1 (2018): 135-142. <http://eudml.org/doc/288464>.

@article{AloysiusGodinho2018,
abstract = {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.},
author = {Aloysius Godinho, Tarkeshwar Singh, S. Arumugam},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {distance magic labeling; distance magic index; S-magic graph; S-magic labeling},
language = {eng},
number = {1},
pages = {135-142},
title = {The Distance Magic Index of a Graph},
url = {http://eudml.org/doc/288464},
volume = {38},
year = {2018},
}

TY - JOUR
AU - Aloysius Godinho
AU - Tarkeshwar Singh
AU - S. Arumugam
TI - The Distance Magic Index of a Graph
JO - Discussiones Mathematicae Graph Theory
PY - 2018
VL - 38
IS - 1
SP - 135
EP - 142
AB - 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.
LA - eng
KW - distance magic labeling; distance magic index; S-magic graph; S-magic labeling
UR - http://eudml.org/doc/288464
ER -

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