Some New Bounds for the Inverse Sum Indeg Energy of Graphs

Let G be a (molecular) graph with n vertices, and di be the degree of its i-th vertex. Then, the inverse sum indeg matrix of G is the n × n matrix C(G) with entries (formula presented), if the i-th and the j-th vertices are adjacent and 0 otherwise. Let µ1 ≥ µ2 ≥ … ≥ µn be the eigenvalues of C arranged in order. The inverse sum indeg energy of G, εisi (G) can be represented as ∑nj=1|µi|. In this paper, we establish several novel upper and lower sharp bounds on µ1 and εisi (G) via some other graph parameters, and describe the structures of the extremal graphs