@article{Xu2025, 
author = {Xin Xu and Xu Zhang and Jiawei Shao},
title = {Planar Turán number of double star        S          3      ,      4},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {1},
pages = {1628-1644},
keywords = {extremal graphs, Turán-type problem, planar graph, double star},
url = {https://www.sciopen.com/article/10.3934/math.2025075},
doi = {10.3934/math.2025075},
abstract = {Planar Turán number, denoted by              e      x                      P              (  n  ,  H  ), is the maximum number of edges in an    n-vertex planar graph which does not contain    H as a subgraph. Ghosh, Győri, Paulos and Xiao initiated the topic of the planar Turán number for double stars. There were two double stars        S          3      ,      4       and        S          3      ,      5       that remained unknown. In this paper, we give the exact value of              e      x                      P              (  n  ,      S          3      ,      4        ).}
}