Let G be a simple graph. We say that a hypergraph \(\cal{H}\) is a Berge-G if there is a bijection \(\psi : E(G)\rightarrow E({\cal{H}}))\) such that e ⊆ ψ(e) for all e ∈ E(G). For any r-uniform hypergraph \(\cal{H}\) and a real number p ≥ 1, the p-spectral radius of \(\cal{H}\) is defined as \({\lambda^{(p)}}({\cal{H}}) = \mathop{\max}\limits_{x \in{\mathbb{R}^n},{{\| x \|}_p} = 1} r\mathop{\sum}\limits_{\{{{i_1},{i_2}, \ldots,{i_r}}\} \in E({\cal{H}})}{x_{{i_1}}}{x_{{i_2}}} \cdots{x_{{i_r}}}.\) A keyring Cn(k) is a graph of order n obtained from a cycle of length n − k by appending k leaves to one of vertices of the cycle. In this paper, we obtain the 3-uniform hypergraphs with maximum p-spectral radius for p ≥ 1 among 3-uniform Berge-G hypergraphs when G is a keyring.
