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Erschienen in:
2011 | OriginalPaper | Buchkapitel
On a Relationship between Completely Separating Systems and Antimagic Labeling of Regular Graphs
verfasst von : Oudone Phanalasy, Mirka Miller, Leanne Rylands, Paulette Lieby
Erschienen in: Combinatorial Algorithms
Verlag: Springer Berlin Heidelberg
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A completely separating system (CSS) on a finite set [
n
] is a collection
$\mathcal C$
of subsets of [
n
] in which for each pair
a
≠
b
∈ [
n
], there exist
$A, B\in\mathcal C$
such that
a
∈
A
,
b
∉
A
and
b
∈
B
,
a
∉
B
.
An antimagic labeling of a graph with
p
vertices and
q
edges is a bijection from the set of edges to the set of integers {1,2, ...,
q
} such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. A graph is antimagic if it has an antimagic labeling.
In this paper we show that there is a relationship between CSSs on a finite set and antimagic labeling of graphs. Using this relationship we prove the antimagicness of various families of regular graphs.