The General Position Problem on Kneser Graphs and on Some Graph Operations
A vertex subset of a graph is a general position set of if no vertex of lies on a geodesic between two other vertices of . The cardinality of a largest general position set of is the general position number (gp-number) gp( ) of . The gp-number is determined for some families of Kneser graphs, in par...
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| Veröffentlicht in: | Discussiones Mathematicae. Graph Theory 2021-11, Vol.41 (4), p.1199-1213 |
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| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | A vertex subset
of a graph
is a general position set of
if no vertex of
lies on a geodesic between two other vertices of
. The cardinality of a largest general position set of
is the general position number (gp-number) gp(
) of
. The gp-number is determined for some families of Kneser graphs, in particular for
2),
≥ 4, and
3),
≥ 9. A sharp lower bound on the gp-number is proved for Cartesian products of graphs. The gp-number is also determined for joins of graphs, coronas over graphs, and line graphs of complete graphs. |
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| ISSN: | 1234-3099 2083-5892 |
| DOI: | 10.7151/dmgt.2269 |