New Bounds on the Triple Roman Domination Number of Graphs
Keyword(s):
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 .
2016 ◽
Vol 10
(1)
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pp. 65-72
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2018 ◽
Vol 5
(2)
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pp. 29-34
2017 ◽
Vol 09
(02)
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pp. 1750023
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