TY - JOUR
T1 - Ring-magic labelings of graphs
AU - Shiu, Wai Chee
AU - Low, Richard M.
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2008/6
Y1 - 2008/6
N2 - In this paper, a generalization of a group-magic graph is introduced and studied. Let R be a commutative ring with unity 1. A graph G = (V, E) is called R-ring-magic if there exists a labeling f: E → R- {0} such that the induced vertex labelings f+: V → R, defined by fx (v) = πf(u,v) where (u,v) ∈ E, and fx: V → R, defined by fx(v) = Πf(u,v) where (u,v) ∈ E, are constant maps. General algebraic results for R-ring-magic graphs are established. In addition, Zn-ring-magic graphs and, in particular, trees are examined.
AB - In this paper, a generalization of a group-magic graph is introduced and studied. Let R be a commutative ring with unity 1. A graph G = (V, E) is called R-ring-magic if there exists a labeling f: E → R- {0} such that the induced vertex labelings f+: V → R, defined by fx (v) = πf(u,v) where (u,v) ∈ E, and fx: V → R, defined by fx(v) = Πf(u,v) where (u,v) ∈ E, are constant maps. General algebraic results for R-ring-magic graphs are established. In addition, Zn-ring-magic graphs and, in particular, trees are examined.
UR - http://ajc.maths.uq.edu.au/?page=get_volumes&volume=41
UR - http://www.scopus.com/inward/record.url?scp=77957676619&partnerID=8YFLogxK
M3 - Journal article
AN - SCOPUS:77957676619
SN - 1034-4942
VL - 41
SP - 147
EP - 158
JO - Australasian Journal of Combinatorics
JF - Australasian Journal of Combinatorics
ER -