Abstract
The planar Turán number of a given graph H, denoted by exP(n,H), is the maximum number of edges over all planar graphs on n vertices that do not contain a copy of H as a subgraph. Let Hk be a friendship graph, which is obtained from k triangles by sharing a vertex. In this paper, we obtain sharp bounds of exP(n,Hk) and exP(n,K1+Pk+1) for all non-trivial cases, which improve the corresponding results of Lan, Shi and Song in ((2019) [9]).
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