Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2015 (2015), Article ID 320616, 7 pages.
On -Vertex-Antimagic Edge Labeling of Regular Graphs
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.
J. Appl. Math., Volume 2015 (2015), Article ID 320616, 7 pages.
First available in Project Euclid: 17 August 2015
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Bača, Martin; Semaničová-Feňovčíková, Andrea; Wang, Tao-Ming; Zhang, Guang-Hui. On $(a,1)$ -Vertex-Antimagic Edge Labeling of Regular Graphs. J. Appl. Math. 2015 (2015), Article ID 320616, 7 pages. doi:10.1155/2015/320616. https://projecteuclid.org/euclid.jam/1439816406