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International Journal of Mathematics and Mathematical Sciences
Volume 2017, Article ID 5156974, 6 pages
https://doi.org/10.1155/2017/5156974
Research Article

New Results on the (Super) Edge-Magic Deficiency of Chain Graphs

1Department of Civil Engineering, Universitas Merdeka Malang, Jl. Taman Agung No. 1, Malang 65146, Indonesia
2School of Computing, Telkom University, Jl. Telekomunikasi No. 1, Bandung 40257, Indonesia

Correspondence should be addressed to Adiwijaya; moc.liamg@ayajiwida.gnak

Received 3 February 2017; Accepted 29 May 2017; Published 12 July 2017

Academic Editor: Dalibor Froncek

Copyright © 2017 Ngurah Anak Agung Gede and Adiwijaya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a graph of order and size . An edge-magic labeling of is a bijection such that is a constant for every edge . An edge-magic labeling of with is called a super edge-magic labeling. Furthermore, the edge-magic deficiency of a graph , , is defined as the smallest nonnegative integer such that has an edge-magic labeling. Similarly, the super edge-magic deficiency of a graph , , is either the smallest nonnegative integer such that has a super edge-magic labeling or if there exists no such integer . In this paper, we investigate the (super) edge-magic deficiency of chain graphs. Referring to these, we propose some open problems.