The extremal $p$-spectral radius of Berge-hypergraphs

Let $G$ be a graph. We say that a hypergraph $H$ is a Berge-$G$ if there is a bijection $\varphi :E(G)\to E(H)$ such that $e\subseteq \varphi (e)$ for all $e\in E(G)$\mathrm{.}Forany$r$-uniformhypergraph$H$andarealnumber$p\geq 1$,the$p$-spectralradius$\lambda^{(p)}(H)$of$H$ is defined as $${\lambda }^{(p)}(H):=\underset{\mathbf{x}\in {\mathbb{R}}^n,\mathrm{\parallel }\mathbf{x}{\mathrm{\parallel }}_p=1}{\max }r\sum _{\{i_1,i_2,\dots ,i_r\}\in E(H)}{x}_{i_1}{x}_{i_2}\cdots x_{i_r}\mathrm{.}$$ In this paper, we study the $p$-spectral radius of Berge-$G$ hypergraphs. We determine the $3$-uniform hypergraphs with maximum $p$-spectral radius for $p\ge 1$ among Berge-$G$ hypergraphs when $G$ is a path, a cycle or a star.