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2015 On ( a , 1 ) -Vertex-Antimagic Edge Labeling of Regular Graphs
Martin Bača, Andrea Semaničová-Feňovčíková, Tao-Ming Wang, Guang-Hui Zhang
J. Appl. Math. 2015: 1-7 (2015). DOI: 10.1155/2015/320616

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.

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Martin Bača. Andrea Semaničová-Feňovčíková. Tao-Ming Wang. Guang-Hui Zhang. "On ( a , 1 ) -Vertex-Antimagic Edge Labeling of Regular Graphs." J. Appl. Math. 2015 1 - 7, 2015. https://doi.org/10.1155/2015/320616

Information

Published: 2015
First available in Project Euclid: 17 August 2015

zbMATH: 07132057
MathSciNet: MR3358357
Digital Object Identifier: 10.1155/2015/320616

Rights: Copyright © 2015 Hindawi

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