On Estrada index of trees

Abstract Let G be a graph on n vertices, and let λ 1 , λ 2 , … , λ n be its eigenvalues. The Estrada index is defined as EE ( G ) = ∑ i = 1 n e λ i . 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 + 1 3 ⌉ , 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 Ilic and Stevanovic in Ref. [14].

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