Discussiones Mathematicae Graph Theory (Feb 2018)

The Distance Magic Index of a Graph

  • Godinho Aloysius,
  • Singh Tarkeshwar,
  • Arumugam S.

DOI
https://doi.org/10.7151/dmgt.1998
Journal volume & issue
Vol. 38, no. 1
pp. 135 – 142

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.

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