Spectral extremal problem for the odd prism

The spectral Turán number $\text{spex}(n,F)$ denotes the maximum spectral radius $\rho (G)$ of an $F$-free graph $G$ of order $n$. This paper determines $\text{spex}(n,C_{2k+1}^{\mathrm{\square }})$ for all sufficiently large $n$, establishing the unique extremal graph. Here, $C_{2k+1}^{\mathrm{\square }}$ is the odd prism – the Cartesian product $C_{2k+1}\mathrm{\square }{K}_2$ – where the Cartesian product $G\mathrm{\square }F$ has vertex set $V(G)\times V(F)$, and edges between $(u_1,v_1)$ and $(u_2,v_2)$ if either $u_1=u_2$ and $v_1{v}_2\in E(F)$, or ($v_1=v_2$ and $u_1{u}_2\in E(G)$).