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For a graphan independent double Roman dominating function (IDRDF) is a functionhaving the property that: (i) every vertexwith  f ( v ) = 0 has a neighbor  u  with  f ( u ) = 3 or at least two neighbors  x  and  y  such that(ii) every vertexwith  f ( v ) = 1 has at least one neighbor assigned a 2 or 3 under  f ; (iii) the set of vertices assigned non-zero values under  f  is independent. The weight of an IDRDF is the sum of its values overs all vertices, and the independent double Roman domination numberis the minimum weight of an IDRDF onIn this article, we show that for every tree  T  of orderwhere  s ( T ) is the number of support vertices of  T , improving the-upper bound established in [Maimani et al. Independent double Roman domination in graphs, Bulletin of the Iranian Mathematical Society, 46 (2020) 543–555]. Moreover, we characterize the trees  T  of orderwith

An improved upper bound on the independent double Roman domination number of trees