New Bounds on the Triple Roman Domination Number of Graphs

M. Hajjari, H. Abdollahzadeh Ahangar, R. Khoeilar, Z. Shao, S. M. Sheikholeslami, Firdous A. Shah
2022 Journal of Mathematics  
In this paper, we derive sharp upper and lower bounds on the sum γ 3 R G + γ 3 R G ¯ and product γ 3 R G γ 3 R G ¯ , where G ¯ is the complement of graph G . We also show that for each tree T of order n ≥ 2 , γ 3 R T ≤ 3 n + s T / 2 and γ 3 R T ≥ ⌈ 4 n T + 2 − ℓ T / 3 ⌉ , where s T and ℓ T are the number of support vertices and leaves of T .
doi:10.1155/2022/9992618 fatcat:lbeornvmtbgsrh6o6cchb5rphe