The energy E of a graph is defined as the sum of the absolute values of its eigenvalues. A graph with n vertices is said to be hypoenergetic if E < n. Li and Ma [X. Li, H. Ma, Hypoenergetic and strongly hypoenergetic k-cyclic graphs, MATCH Commun. Math. Comput. Chem. 64 (2010) 41-60] studied hypoenergetic k-cyclic graphs. They showed that there exist hypoenergetic unicyclic, bicyclic, and tricyclic graphs for all π and the maximum degree δ > 4, except in the following cases of δ = 4, for which they did not determine whether or not there exist hypoenergetic graphs: (i) n = 13 for unicyclic graphs; (ii) n = 8,10,11,12,14,15 for bicyclic graphs and (iii) n = 8,9,11,12,15 for tricyclic graphs. In this paper, we complete the solution of these problems, and show that there are no hypoenergetic graphs for all these cases.
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