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

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.