Extremal Edge General Position Sets in Some Graphs

A set of edges X ⊆ E ( G ) of a graph G is an edge general position set if no three edges from X lie on a common shortest path. The edge general position number gp e ( G ) of G is the cardinality of a largest edge general position set in G . Graphs G with gp e ( G ) = | E ( G ) | - 1 and with gp e (...

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Veröffentlicht in:Graphs and combinatorics 2024-04, Vol.40 (2), Article 40
Hauptverfasser: Tian, Jing, Klavžar, Sandi, Tan, Elif
Format: Artikel
Sprache:eng
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Zusammenfassung:A set of edges X ⊆ E ( G ) of a graph G is an edge general position set if no three edges from X lie on a common shortest path. The edge general position number gp e ( G ) of G is the cardinality of a largest edge general position set in G . Graphs G with gp e ( G ) = | E ( G ) | - 1 and with gp e ( G ) = 3 are respectively characterized. Sharp upper and lower bounds on gp e ( G ) are proved for block graphs G and exact values are determined for several specific block graphs.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-024-02770-z