In:
Journal of Applied Mathematics, Hindawi Limited, Vol. 2015 ( 2015), p. 1-7
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.
Type of Medium:
Online Resource
ISSN:
1110-757X
,
1687-0042
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2015
detail.hit.zdb_id:
2578385-3
SSG:
17,1
