Let G be a graph. A hypergraph \(H^{*}\) is called a Berge-G if there is a bijection \(\phi : E(G)\rightarrow E(H^{*})\) such that \(e\subseteq \phi (e)\) for all \(e\in E(G)\) , where \(E(\cdot )\) is the set of edges. A hypergraph H is said to be Berge-G free if H does not contain a Berge-G as its subhypergraph. Let \(k\geqslant 3\) and \(n\geqslant 5\) . For the connected linear k-uniform hypergraphs on n vertices without the Berge- \(\{C_3,K_{2,3}\}\) or the Berge- \(\{F_2,K_{2,3}\}\) , the upper bounds of their spectral radii regarding to n and k are derived, where \(C_3\) is a cycle of length 3, \(F_2\) a graph obtained from two disjoint \(C_3\) by identifying a vertex of \(C_3\) with a vertex of another \(C_3\) , and \(K_{2,3}\) a complete bipartite graph with two parts of sizes 2 and 3.
