Authors:
S. Arumugam, A. Godinho, T. Singh
Title:
The distance magic index od a graph
Source:
Discussiones Mathematicae Graph Theory
Received 28.06.2016, Revised 20.10.2016, Accepted 20.10.2016, doi: 10.7151/dmgt.1998

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)=\minα (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

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