On the inverse sum indeg energy of trees

Abstract

Let [Formula: see text] be a graph of order [Formula: see text] and [Formula: see text] be the degree of the vertex [Formula: see text], for [Formula: see text]. The [Formula: see text] matrix of [Formula: see text] is the square matrix of order [Formula: see text] whose [Formula: see text]-entry is equal to [Formula: see text] if [Formula: see text] is adjacent to [Formula: see text], and zero otherwise. Let [Formula: see text], be the eigenvalues of [Formula: see text] matrix. The [Formula: see text] energy of a graph [Formula: see text], denoted by [Formula: see text], is defined as the sum of the absolute values of the eigenvalues of [Formula: see text] matrix. In this paper, we prove that the star has the minimum [Formula: see text] energy among trees.