The planar Tur\'an number of double star S2,4

Planar Tur\'an number exP(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, Gy{o}ri, Paulos and Xiao initiated the topic of the planar Tur\'an number for double stars. In this paper, we prove that exP(n,S2,4)≤ 31/14n for n≥ 1, and show that equality holds for infinitely many integers n.