@article{Song2022, 
author = {Xiaodi Song and Jianping Li and Jianbin Zhang and Weihua He},
title = {Trees with the second-minimal ABC energy},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {10},
pages = {18323-18333},
keywords = {energy, tree, ABC energy, ABC matrix, ABC eigenvalues},
url = {https://www.sciopen.com/article/10.3934/math.20221009},
doi = {10.3934/math.20221009},
abstract = {The atom-bond connectivity energy (ABC energy) of an undirected graph    G, denoted by              E              A      B      C        (  G  ), is defined as the sum of the absolute values of the ABC eigenvalues of    G. Gao and Shao [The minimum ABC energy of trees, Linear Algebra Appl., 577 (2019), 186-203] proved that the star        S    n   is the unique tree with minimum ABC energy among all trees on    n vertices. In this paper, we characterize the trees with the minimum ABC energy among all trees on    n vertices except the star        S    n  .}
}