Minors play a key role in graph theory, and extremal problems on forbidding minors have attracted appreciable amount of interest in the past decades. In this paper, we focus on spectral extrema of $K_{s,t}$-minor free graphs, and determine extremal graphs with maximum spectral radius over all $K_{s,t}$-minor free graphs of sufficiently large order. This generalizes and improves several previous results. For $t\ge s\ge 2$, our result completely solves Tait's conjecture. For $t\ge s=1$, our result gives a spectral analogue of a theorem due to Ding, Johnson and Seymour, which determines the maximum number of edges in $K_{1,t}$-minor free connected graphs. Some spectral and structural tools, such as, local edge maximality, local degree sequence majorization and double eigenvectors transformation, are used to characterize structural properties of extremal graphs.

未成年人在图论中起着关键作用，在过去的几十年中，禁止未成年人的极端问题引起了相当多的兴趣。在本文中，我们关注的是谱极值${ķ}_{s,吨}$- 次要自由图，并确定具有最大光谱半径的极值图${ķ}_{s,吨}$- 足够大阶的次要自由图。这概括并改进了几个先前的结果。为了$吨\ge s\ge 2$，我们的结果完全解决了泰特猜想。为了$吨\ge s=1$，我们的结果给出了 Ding、Johnson 和 Seymour 定理的谱类比，它确定了边缘的最大数量${ķ}_{1,吨}$- 次要的自由连通图。一些谱和结构工具，例如局部边缘最大值、局部度数序列主要化和双特征向量变换，用于表征极值图的结构特性。