On a conjecture on the tree with fourth greatest energy

摘要

In [6], Ivan Gutman et al. conjectured that the tree P_n(2, 6, n -9) of order n ≥ 14 has the fourth greatest energy among all trees of order n. By using the method of "quasi-order ?", two of the present authors [8] claimed to have proved this conjecture by showing that T ? P _n(2, 6, n-9) for all trees T of order n with T ? {P _n,P_n(2, 2, n - 5), P_n(2, 4, n-7), P _n(2,6,n-9)