New Bounds on the Triple Roman Domination Number of Graphs
M. Hajjari, Hossein Abdollahzadeh Ahangar, Rana Khoeilar, Zehui Shao, Seyed Mahmoud Sheikholeslami · Journal of Mathematics · 2022
In this paper, we derive sharp upper and lower bounds on the sum and product , where is the complement of graph G. We also show that for each tree T of order n ≥ 2, γ[3R](T) ≤ 3n + s(T)/2 and γ[3R](T) ≥ ⌈4(n(T) + 2 − ℓ(T))/3⌉, where s(T) and ℓ(T) are the number of support vertices and leaves of T.