Abstract
Let H be a hypergraph with n vertices. The Estrada index of H is defined as the sum of eλ1,…,eλn, where λ1,…,λn are the eigenvalues of the adjacency matrix of H. Let Tn,r be the set of r-uniform linear hypertrees with n vertices and Tn,rΔ the subset of Tn,r in which each hypergraph has a largest vertex degree Δ, where r ≥ 3 and 2≤Δ≤(n−1)(r−1). Several new transformations for studying the Estrada indices of hypergraphs are introduced. By these transformations, the hypertree with the smallest Estrada index is determined in Tn,rΔ and the hypertrees with the smallest, the second smallest, the largest, and the second largest Estrada indices are derived among Tn,r.
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