Some New Bounds for the Inverse Sum Indeg Energy of Graphs

Abstract

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 cij=didjdi+dj, 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 ∑j=1n|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.