Journal of Applied Mathematics

On ( a , 1 ) -Vertex-Antimagic Edge Labeling of Regular Graphs

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

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Abstract

An ( a , s ) -vertex-antimagic edge labeling (or an ( a , s ) -VAE labeling, for short) of G is a bijective mapping from the edge set E ( G ) of a graph G to the set of integers 1,2 , , | E ( G ) | with the property that the vertex-weights form an arithmetic sequence starting from a and having common difference s , where a and s 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 ( a , s ) -antimagic if it admits an ( a , s ) -VAE labeling. In this paper, we investigate the existence of ( a , 1 ) -VAE labeling for disconnected 3-regular graphs. Also, we define and study a new concept ( a , s ) -vertex-antimagic edge deficiency, as an extension of ( a , s ) -VAE labeling, for measuring how close a graph is away from being an ( a , s ) -antimagic graph. Furthermore, the ( a , 1 ) -VAE deficiency of Hamiltonian regular graphs of even degree is completely determined. More open problems are mentioned in the concluding remarks.

Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 320616, 7 pages.

Dates
First available in Project Euclid: 17 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1439816406

Digital Object Identifier
doi:10.1155/2015/320616

Mathematical Reviews number (MathSciNet)
MR3358357

Citation

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


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