New Bounds on the Triple Roman Domination Number of Graphs - M. Hajjari; H. Abdollahzadeh Ahangar; R. Khoeilar; Z. Shao; S. M. Sheikholeslami (Journal of Mathematics)
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.