Abstract
Let G be a graph on n vertices, and let λ1,λ2,…,λn be its eigenvalues. The Estrada index is defined as EE(G)=∑i=1neλi. We determine the unique tree with maximum Estrada index among the trees on n vertices with given matching number, and the unique tree with maximum Estrada index among the trees on n vertices with fixed diameter. For Δ⩾⌈n+13⌉, we also determine the tree with maximum Estrada index among the trees on n vertices with maximum degree Δ. It gives a partial solution to the conjecture proposed by Ilić and Stevanović in Ref. [14].
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