Graphs with Large Steiner Number
In 2002, G. Chartrand and P. Zhang [ Discrete Math. , 242 , 4 (2002)] characterized the connected graphs G of order p ≥ 3 with Steiner number p, p − 1 , or 2 . We characterize all connected graphs G of order p ≥ 4 with Steiner number s ( G ) = p − 2. In addition, we obtain some sharp Nordhaus–Gaddum...
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| Veröffentlicht in: | Ukrainian mathematical journal 2024-10, Vol.76 (5), p.805-815 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In 2002, G. Chartrand and P. Zhang [
Discrete Math.
,
242
, 4 (2002)] characterized the connected graphs
G
of order
p
≥ 3 with Steiner number
p, p −
1
,
or 2
.
We characterize all connected graphs
G
of order
p
≥ 4 with Steiner number
s
(
G
) =
p −
2. In addition, we obtain some sharp Nordhaus–Gaddum bounds for the Steiner number of connected graphs whose complement is also connected. |
|---|---|
| ISSN: | 0041-5995 1573-9376 |
| DOI: | 10.1007/s11253-024-02354-3 |