On inverse sum indeg energy of graphs

For a simple graph with vertex set {v1, v2, ⋯, vn} and degree sequence dvi i = 1, 2, ⋯, n the inverse sum indeg matrix (ISI matrix) AISI(G) = (aij) of G is a square matrix of order n, where aij = dvidvj/dvi + dvj, if vi is adjacent to vj and 0, otherwise. The multiset of eigenvalues τ1 ≥ τ2 ≥ ⋯ ≥ τn of AISI(G) is known as the ISI spectrum of G. The ISI energy of G is the Σni=1 |τ| of the absolute ISI eigenvalues of G. In this article, we give some properties of the ISI eigenvalues of graphs. Also, we obtain the bounds of the ISI eigenvalues and characterize the extremal graphs. Furthermore, we construct pairs of ISI equienergetic graphs for each n≥ 9.