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Let G = (V_G, E_G) be a simple and connected graph. The eccentric connectivity index of G is represented as ξ^c(G) = Σ_x∈VG deg_G(x)ec_G(x), where deg_G(x) and ec_G(x) represent the degree and the eccentricity of x, respectively. The eccentric adjacency index of G is represented as ξ^ad(G) = Σ_x∈VG (S_G(x)/ec_G(x)), where SQ(x) is the sum of degrees of neighbors of x. In this paper, we determine the trees with the smallest eccentric connectivity index when bipartition size, independence number, and domination number are given. Furthermore, we discuss the trees with the largest eccentric adjacency index when bipartition size, matching number, and independence number are given.