Spectral extremal problem for the odd prism

Xinhui Duan; Lu Lu

paper

Spectral extremal problem for the odd prism

arXiv:2507.01266

Abstract

The spectral TurÃ¡n number $\spex(n, F)$ denotes the maximum spectral radius $I ¨ (G)$ of an $F$ -free graph $G$ of order $n$ . This paper determines $\spex\left(n, C_{2k+1}^{\square}\right)$ for all sufficiently large $n$ , establishing the unique extremal graph. Here, $C_{2 k + 1}^{□}$ is the odd prism -- the Cartesian product $C_{2 k + 1} □ K_{2}$ -- where the Cartesian product $G □ F$ 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 $u_{1} u_{2} \in E (G)$ ).