Spectral extremal problem for the odd prism

2025/07/02 by Lu Lu, Duan, Xinhui, Lu, Lu
Mathematics · #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2507.01266

openalex publication_date 2025/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The spectral Turán number \spex(n, F) denotes the maximum spectral radius ρ(G) of an F-free graph G of order n. This paper determines \spex(n, C_2k+1^\square) for all sufficiently large n, establishing the unique extremal graph. Here, C_2k+1^\square is the odd prism -- the Cartesian product C_2k+1 \square K₂ -- where the Cartesian product G \square F has vertex set V(G) × V(F), and edges between (u₁,v₁) and (u₂,v₂) if either u₁ = u₂ and v₁v₂ ∈ E(F), or (v₁ = v₂ and u₁u₂ ∈ E(G)).

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