A NOTE ON EXTREMAL VALUES OF THE SCATTERING NUMBER

A NOTE ON EXTREMAL VALUES OF THE SCATTERING NUMBER

Letc(H) denote the number of components of graphH. The scattering number of a graphGis the maximum ofc(G−S) − |S| taken over all cut-setsSofG. In this note we explore the minimum and maximum scattering number for several families. For example, we show that the minimum scattering number of a triangle...

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Veröffentlicht in:Taiwanese journal of mathematics 2013-10, Vol.17 (5), p.1651-1658
Hauptverfasser: Dankelmann, Peter, Goddard, Wayne, McPillan, Charles A., Swart, Henda C.
Format: Artikel
Sprache:eng
Schlagworte:
Binomial trees
Cartesianism
Graph theory
Mathematical minima
Planar graphs
Plant spines
Tensors
Toughness
Vertices
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Zusammenfassung:Letc(H) denote the number of components of graphH. The scattering number of a graphGis the maximum ofc(G−S) − |S| taken over all cut-setsSofG. In this note we explore the minimum and maximum scattering number for several families. For example, we show that the minimum scattering number of a triangle-free graph onnvertices is approximately −n/3. We also consider the scattering number of some graph products. 2010Mathematics Subject Classification: 05C40, 05C42. Key words and phrases: Scattering number, Graph, Toughness, Triangle-free.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.17.2013.2583