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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Bibliographic Details
Published inGraphs and combinatorics Vol. 40; no. 2
Main Authors Tian, Jing, Klavžar, Sandi, Tan, Elif
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.04.2024
Springer Nature B.V
Subjects
Combinatorics
Engineering Design
Graph theory
Graphs
Lower bounds
Mathematics
Mathematics and Statistics
Original Paper
Shortest-path problems
Diametral path
05C12
Block graph
General position set
Edge general position set
05C35
Cut-vertex
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Summary: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