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Journal of Applied Mathematics - Volume 2015 2015, Article ID 320616, 7 pages -

Research Article

Department of Applied Mathematics and Informatics, Technical University, Letná 9, 04200 Košice, Slovakia

Department of Applied Mathematics, Tunghai University, Taichung 40704, Taiwan

Department of Applied Mathematics, National Chung Hsing University, Taichung 402, Taiwan

Received 1 April 2015; Accepted 26 May 2015

Academic Editor: Heping Zhang

Copyright © 2015 Martin Bača et al. 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

An -vertex-antimagic edge labeling or an -VAE labeling, for short of is a bijective mapping from the edge set of a graph to the set of integers with the property that the vertex-weights form an arithmetic sequence starting from and having common difference , where and are two positive integers, and the vertex-weight is the sum of the labels of all edges incident to the vertex. A graph is called -antimagic if it admits an -VAE labeling. In this paper, we investigate the existence of -VAE labeling for disconnected 3-regular graphs. Also, we define and study a new concept -vertex-antimagic edge deficiency, as an extension of -VAE labeling, for measuring how close a graph is away from being an -antimagic graph. Furthermore, the -VAE deficiency of Hamiltonian regular graphs of even degree is completely determined. More open problems are mentioned in the concluding remarks.





Autor: Martin Bača, Andrea Semaničová-Feňovčíková, Tao-Ming Wang, and Guang-Hui Zhang

Fuente: https://www.hindawi.com/



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