Perfect Double Roman Domination of Trees by Ayotunde Tolulope Egunjobi A perfect double Roman dominating function of a graph G, abbreviated PDRDfunction, is a function f : V (G) → {0, 1, 2, 3} satisfying the conditions that if f (u) = 0, then u is adjacent to exactly two vertices in V 2 and no vertex in V 3 or exactly one vertex in V 3 and no vertex in V 2 and if f (u) = 1, then u is adjacent to exactly one vertex in V 2 and no vertex in V 3 . The perfect double Roman domination number, denoted γ p dR (G), is the minimum weight of a PDRD-function of G. We prove that if
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