On (a, 1)‐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, issue 1

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.

Date: 2015
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https://doi.org/10.1155/2015/320616

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2015:y:2015:i:1:n:320616

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