An improved upper bound for planar Turán number of double star [formula omitted].

The planar Turán number of a graph H , denoted by e x P (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 e x P (n , S 2 , 5) ≤ 20 7 n. In this paper, we continue to study this and give a better upper bound e x P (n , S 2 , 5) ≤ 19 7 n − 18 7 for all n ≥ 1 , with equality when n = 12. This improves Ghosh's result. [ABSTRACT FROM AUTHOR]