发表机构
Okegawa City Okegawa West Junior High School; Department of Electrical and Computer Engineering, University of New Mexico（尾张野市尾张野西初中; 新墨西哥大学电气与计算机工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用边缺陷矩阵和交互数推导稳定性不等式，对完全图删边后的生成树计数进行高阶排序，确定了生成树最多的九个删除图，并揭示交互数与生成树减少的关系。
AI 中文摘要
本文研究了从完全图中删除固定数量的边所得到的图，按生成树数量进行的高阶排序。利用由被删除的边确定的边缺陷矩阵以及衡量它们之间局部重叠的交互数，我们推导出一个稳定性不等式，该不等式定量估计了与匹配删除情形相比生成树数量的减少。将该稳定性估计与交互数较小的删除图的分类相结合，我们确定了在p≥6且n≥2p时，生成树数量最多的九个删除图（在同构意义下）。我们还通过归一化生成树数量的对数展开，阐明了交互数、删除图的局部结构以及生成树数量减少之间的关系。
英文摘要
In this paper, we study the higher-order ranking, by spanning-tree count, of graphs obtained from a complete graph by deleting a fixed number of edges. Using the edge-defect matrix determined by the deleted edges and the interaction number measuring the local overlap among them, we derive a stability inequality that quantitatively estimates the decrease in the number of spanning trees from the matching-deletion case. Combining this stability estimate with a classification of deletion graphs having small interaction number, we determine, up to isomorphism, the nine deletion graphs with the largest spanning-tree counts for $p\geq6$ and $n\geq2p$. We also clarify the relation between the interaction number, the local structure of the deletion graph, and the decrease in the number of spanning trees through a logarithmic expansion of the normalized spanning-tree count.
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