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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Bibliographic Details
Published inDiscussiones Mathematicae. Graph Theory Vol. 41; no. 4; pp. 1199 - 1213
Main Authors Ghorbani, Modjtaba, Maimani, Hamid Reza, Momeni, Mostafa, Mahid, Farhad Rahimi, Klavžar, Sandi, Rus, Gregor
Format Journal Article
LanguageEnglish
Published Sciendo 01.11.2021
University of Zielona Góra
Subjects
05C12
05C69
05C76
Cartesian product of graphs
corona over graphs
general position set
Kneser graphs
line graphs
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Summary: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.
ISSN:1234-3099
2083-5892
DOI:10.7151/dmgt.2269