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The planar Tur\'an number of a graph H, denoted by ex (n, H), is the maximum number of edges in an n-vertex H-free planar graph. Recently, D. Ghosh, et al. initiated the topic of double stars and prove that ex (n, S₂, ₅) 207n. In this paper, we continue to study this and give a sharp upper bound ex (n, S₂, ₅) 197n-187 for all n 1, with equality when n=12. This improves Ghosh's result.
Xu et al. (Wed,) studied this question.
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