Let G be a graph and λ_1, λ_2,...λ_n be its eigenvalues. Then the energy of G is defined as E(G) = |λ_1| + |λ_2| +... |λ_n|. Let ?(n) be the class of bipartite bicyclic graphs on n vertices containing a cycle with length congruent to 2 modulo 4. In [Z. Liu, B. Zhou, Minimal energies of bipartite bicyclic graphs, MATCH Commun. Math. Comput Chem. 59 (2008) 381-396] it was an attempted to determine the graph that has the minimal energy in ?(n),but left two kinds of graphs B_n~1 and B_n~2 without determining which has the minimal energy. Let g_n be the class of tricyclic graphs G on n vertices that contain no disjoint odd cycles C_p, C_q of lengths p and q with p + q ≡ 2 (mod 4). In [S. Li, X. Li, Z. Zhu, On tricyclic graphs with minimal energy, MATCH Commun. Math. Comput Chem 59 (2008) 397-419] it was attempted to characterize the minimal and second-minimal energies of graphs in g_n, but left four kinds of graphs R_n, W_n, S_n, and Q_n without determining their ordering. This paper is to solve the two unsolved problems completely, and obtain that in g_n, G_n~0, and G_n~1 have the minimal and second-minimal energy for n ≥ 10, respectively, and in ?_n, B_n~1 has the minimal energy for n ≥ 31, otherwise, B_n~2 for n > 31. The methods we use is different from those previously used. One is the approximate root method and the other is the well-known Coulson integral formula.
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