发表机构
College of Sciences, National University of Defense Technology（国防科技大学理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对指定最大度的色临界图，确定了无F图中具最大邻接谱半径的图，是相关边定理的谱对应，推广了团结果，为不平衡谱Turán问题提供基准。
AI 中文摘要
设F是满足χ(F)=r+1≥4的连通色临界图，记S_{n,Δ}^{(r)}=(n−Δ)K₁∨T(Δ,r−1)。我们确定了所有n顶点、指定最大度Δ的无F图中，具有最大邻接谱半径的图。存在常数s_F∈[0,1)，使得对所有足够大的n，当⌈(r−1)n/r⌉≤Δ≤n−Θ(n^{s_F})时，每个Δ(G)=Δ的n顶点无F图G满足ρ(G)≤ρ(S_{n,Δ}^{(r)})，等号成立当且仅当G≅S_{n,Δ}^{(r)}。这是[European J. Combin. 106 (2022), 103576]中边定理的谱对应，推广了[arXiv:2608.26634, 2026]中的团结果，还为其他极值参数产生的不平衡谱Turán问题提供了基准。
英文摘要
Let $F$ be a connected color-critical graph with $χ(F)=r+1\ge4$, let $S_{n,Δ}^{(r)}=(n-Δ)K_1\vee T(Δ,r-1)$. We determine the graph of maximum adjacency spectral radius among all $n$-vertex $F$-free graphs with prescribed maximum degree $Δ$. There is a constant $s_F\in[0,1)$ such that, for all sufficiently large $n$, $\left\lceil\frac{(r-1)n}{r}\right\rceil\le Δ\le n-Θ(n^{s_F})$ implies that every $n$-vertex $F$-free graph $G$ with $Δ(G)=Δ$ satisfies $ρ(G)\le ρ\bigl(S_{n,Δ}^{(r)}\bigr)$, with equality if and only if $G\cong S_{n,Δ}^{(r)}$. This is the spectral counterpart of the edge theorem of [European J. Combin. 106 (2022), 103576.] and extends the clique result in [arXiv:2608.26634, 2026.]. This result also provides a benchmark for unbalanced spectral Turán problems arising from other extremal parameters.
