Extremal Edge General Position Sets in Some Graphs

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Tian J., Klavžar S., Tan E.

Graphs and Combinatorics, cilt.40, sa.2, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s00373-024-02770-z
  • Dergi Adı: Graphs and Combinatorics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: 05C12, 05C35, Block graph, Cut-vertex, Diametral path, Edge general position set, General position set
  • Ankara Üniversitesi Adresli: Evet

Özet

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 gpe(G) of G is the cardinality of a largest edge general position set in G. Graphs G with gpe(G)=|E(G)|-1 and with gpe(G)=3 are respectively characterized. Sharp upper and lower bounds on gpe(G) are proved for block graphs G and exact values are determined for several specific block graphs.