Abstract
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.
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Phanalasy, O., Miller, M., Rylands, L., Lieby, P. (2011). On a Relationship between Completely Separating Systems and Antimagic Labeling of Regular Graphs. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2010. Lecture Notes in Computer Science, vol 6460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19222-7_24
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