LAUSR

Abstract Let G be a graph of order n, and d i be the degree of its i-th vertex. The ABC matrix of G is the matrix of order n whose ( i , j ) -entry is equal to ( d i + d j − 2 ) / ( d i d j ) if the i-th vertex and the j-th vertex of G are adjacent, and 0 otherwise. The ABC eigenvalues of G are the eigenvalues of its ABC matrix, and the ABC energy of G is the sum of the absolute values of its ABC eigenvalues. In Chen (2018) [9] , the author conjectured that the star has the minimum ABC energy among all trees. In this paper, we prove the conjecture is true.