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Planar Tur\'an number ex (n, H) of H is the maximum number of edges in an n-vertex planar graph which does not contain H as a subgraph. Ghosh, Gyori, Paulos and Xiao initiated the topic of the planar Tur\'an number for double stars. In this paper, we prove that ex (n, S₂, ₄) 3114n for n 1, and show that equality holds for infinitely many integers n.
Xu et al. (Mon,) studied this question.