New Bounds on the Triple Roman Domination Number of Graphs

In this paper, we derive sharp upper and lower bounds on the sum γ3RG+γ3RG¯ and product γ3RGγ3RG¯, where G¯ is the complement of graph G. We also show that for each tree T of order n≥2, γ3RT≤3n+sT/2 and γ3RT≥⌈4nT+2−ℓT/3⌉, where sT and ℓT are the number of support vertices and leaves of T....

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Journal of mathematics (Hidawi) 2022, Vol.2022 (1)
Hauptverfasser:	Hajjari, M., Ahangar, H. Abdollahzadeh, Khoeilar, R., Shao, Z., Sheikholeslami, S. M.
Format:	Artikel
Sprache:	eng
Schlagworte:	Apexes Equality Graphs Lower bounds Mathematics Neighborhoods Roman civilization
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	In this paper, we derive sharp upper and lower bounds on the sum γ3RG+γ3RG¯ and product γ3RGγ3RG¯, where G¯ is the complement of graph G. We also show that for each tree T of order n≥2, γ3RT≤3n+sT/2 and γ3RT≥⌈4nT+2−ℓT/3⌉, where sT and ℓT are the number of support vertices and leaves of T.
ISSN:	2314-4629 2314-4785
DOI:	10.1155/2022/9992618