均匀超图的迹及其在Estrada指标中的应用
The trace of uniform hypergraphs with application to Estrada index
AI总结：
本文研究超图邻接张量的迹，给出超树和线性单圈超图的迹的新表达式及割点扰动结果，并据此确定固定边数和完美匹配下Estrada指标最大的唯一超树，以及固定边数和围长3下Estrada指标最大的唯一单圈超图。
摘要：
本文研究超图邻接张量的迹（简称为超图的迹）。我们通过赋予连通子超图的权函数，给出了超树和线性单圈超图的迹的新表达式，并对具有割点的超图的迹提供了一些扰动结果。作为应用，我们在所有具有固定边数和完美匹配的超树中确定了具有最大Estrada指标的唯一超树，并在所有具有固定边数和围长3的单圈超图中确定了具有最大Estrada指标的唯一单圈超图。
英文摘要：
In this paper we investigate the traces of the adjacency tensor of hypergraphs (simply called the traces of hypergraphs). We give new expressions for the traces of hypertrees and linear unicyclic hypergraphs by the weight function assigned to their connected sub-hypergraphs, and provide some perturbation results for the traces of a hypergraph with cut vertices. As applications we determine the unique hypertree with maximum Estrada index among all hypertrees with fixed number of edges and perfect matchings, and the unique unicyclic hypergraph with maximum Estrada index among all unicyclic hypergraph with fixed number of edges and girth $3$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
