Bounds of the Sum-connectivity Energy of Graphs

Abstract

The sum-connectivity energy of a graph is defined as the sum of the absolute value of all the eigenvalues of its sum-connectivity matrix. In this paper, we give further lower and upper bounds for the sum-connectivity energy in terms of the number of vertices, number of edges, the harmonic index, and determinant of the sum-connectivity matrix. We also show that among connected graphs with $n$ vertices, the star graph $K_{1,n-1}$ has the minimum sum-connectivity energy.