An improved upper bound for planar Tur\'an number of double star S2,5

The planar Tur\'{a}n number of a graph H, denoted by exP(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 exP(n,S2,5)≤ 20/7n. In this paper, we continue to study this and give a sharp upper bound exP(n,S2,5)≤ 19/7n-18/7 for all n≥ 1, with equality when $n=12$. This improves Ghosh's result.