On inverse sum indeg energy of graphs

Abstract For a simple graph with vertex set { v 1 , 2 … n } \left\{{v}_{1},{v}_{2},\ldots ,{v}_{n}\right\} and degree sequence d i = , {d}_{{v}_{i}}\hspace{0.33em}i=1,2,\ldots ,n , the inverse sum indeg matrix (ISI matrix) A ISI ( G ) a j {A}_{{\rm{ISI}}}\left(G)=\left({a}_{ij}) of G is square order n, where + {a}_{ij}=\frac{{d}_{{v}_{i}}{d}_{{v}_{j}}}{{d}_{{v}_{i}}+{d}_{{v}_{j}}}, if {v}_{i} adjacent to {v}_{j} 0, otherwise. The multiset eigenvalues τ ≥ form="prefix">≥ ⋯ {\tau }_{1}\ge }_{2}\hspace{0.33em}\ge \cdots \ge }_{n} {A}_{{\rm{ISI}}}\left(G) known as ISI spectrum . energy ∑ ∣ \mathop{\sum }\limits_{i=1}^{n}| }_{i}| absolute . G. In this article, we give some properties graphs. Also, obtain bounds characterize extremal Furthermore, construct pairs equienergetic graphs for each 9 n\ge 9