On (a, 1)-Vertex-Antimagic Edge Labeling of Regular Graphs. (8th June 2015)

• Record Type: Journal Article
• Authors: Bača, Martin; Semaničová-Feňovčíková, Andrea; Wang, Tao-Ming; Zhang, Guang-Hui
• Other Names: Zhang Heping Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2015(2015)
• Publication Date: 2015-06-08
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2015/320616
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : An( a, s ) - vertex-antimagic edge labeling (or an( a, s ) - VAE labeling, for short) ofG is a bijective mapping from the edge setE ( G ) of a graphG to the set of integers1, 2, …, | E ( G ) | with the property that the vertex-weights form an arithmetic sequence starting froma and having common differences, wherea ands 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.