On -Vertex-Antimagic Edge Labeling of Regular Graphs

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

Journal of Applied Mathematics, 2015, vol. 2015, 1-7

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.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:320616

DOI: 10.1155/2015/320616

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