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 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
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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. |
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ISSN: | 0911-0119 1435-5914 |
DOI: | 10.1007/s00373-024-02770-z |