Planar Tur\'an number for balanced double stars

Planar Tur\'an number, denoted by exP(n,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. For balanced double star, S3,3 is the only remaining graph need to be considered. In this paper, we give the exact value of exP(n,S3,3), forcing the planar Tur\'an number for all balanced double stars completely determined.