On a conjecture about the hypoenergetic trees

The energy E ( G ) of a graph G is the sum of the absolute values of the eigenvalues of G . An n -vertex graph G is said to be hypoenergetic if E ( G ) < n . In Gutman et al. (2008) [14] the authors conjectured that there exist n -vertex hypoenergetic trees with maximum degree Δ = 4 for any n ≡ 2 mod 4, n > 2 . In this paper we confirm this conjecture.