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Given a graph $H$ and an integer $p$ ($p\geq 2$), the edge blow-up $H^{p+1}$of $H$ is the graph obtained from replacing each edge in $H$ by a clique oforder $(p+1)$, where the new vertices of the cliques are all distinct. TheTur\'{a}n numbers for edge blow-up of matchings were first studied by Erd\H{o}sand Moon. Very recently some substantial progress of the extremal graphs for$H^{p+1}$ of larger $p$ has been made by Yuan. The range of Tur\'{a}n numbersfor edge blow-up of all bipartite graphs when $p\geq 3$ and the exact Tur\'{a}nnumbers for edge blow-up of all non-bipartite graphs when $p\geq \chi(H) +1$has been determined by Yuan (2022), where $\chi(H)$ is the chromatic number of$H$. A lollipop $C_{k,\;\ell}$ is the graph obtained from a cycle $C_k$ byappending a path $P_{\ell+1}$ to one of its vertices. In this paper, weconsider the extremal graphs for $C_{k,\;\ell}^{p+1}$ of the rest cases $p=2$and $p=3$.

Extremal graphs for edge blow-up of lollipops