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We give new expressions for the traces of hypertrees and linear unicyclic hypergraphs by the weight function assigned to their connected sub-hypergraphs, and present some perturbation results for the traces of a hypergraph when its structure is locally changed. As an application we determine the unique hypertree with maximum Estrada index among all hypertrees with perfect matchings and given number of edges, and the unique unicyclic hypergraph with maximum Estrada index among all unicyclic hypergraph with girth [Formula: see text] and given number of edges. <\/jats:p>","DOI":"10.1142\/s1793830923500659","type":"journal-article","created":{"date-parts":[[2023,7,28]],"date-time":"2023-07-28T16:05:28Z","timestamp":1690560328000},"source":"Crossref","is-referenced-by-count":0,"title":["The trace of uniform hypergraphs with application to Estrada index"],"prefix":"10.1142","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2664-8625","authenticated-orcid":false,"given":"Yi-Zheng","family":"Fan","sequence":"first","affiliation":[{"name":"Center for Pure Mathematics, School of Mathematical Sciences, Anhui University, Hefei 230601, P. R. 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