Given a family \(\mathcal{H}\) of graphs, the planar Turán number of \(\mathcal{H}\) , denoted by \(ex_{\cal{P}}(n,\cal{H})\) , is the maximum number of edges in an n-vertex planar graph not containing any graph in \(\mathcal{H}\) as a subgraph. Ghosh, Győri, Paulos and Xiao initiated the study of planar Turán number for double stars. We obtain an upper bound for \(ex_{\cal{P}}(n,\{S_{2,4},T_{7}^{-}\})\) , where T 7 − is a certain graph obtained from a plane triangulation on 7 vertices by deleting an edge. The bound is tight for in finitely many integers n.
