On Zagreb eccentricity indices of trees with perfect matchings

For a connected graph G with vertex set V (G) and edge set E(G), the first Zagreb eccentricity index and the second Zagreb eccentricity index are defined as 1(G) = vV (G) e 2 (v) and 2(G) = vuE(G) e(v)e(u), respectively, where e(u) is the eccentricity of vertex u in G.In this paper, we identify the trees that minimize the first and second Zagreb eccentricity indices among all trees with 2n vertices and a perfect matching.