Spectral properties of inverse sum indeg index of graphs

The inverse sum indeg (ISI) index is a vertex-degree-based topological index that was selected by Vukičević and Gašperov in 2010 as a significant predictor of the total surface area of octane isomers. One of the main aims of algebraic graph theory is to determine how, or whether, properties of graphs are reflected in the algebraic properties of some matrices. The aim of this paper is to study the ISI index from an algebraic viewpoint. We introduce suitably modified versions of the classical adjacency matrix and the Laplacian matrix involving the degrees of the vertices of a graph. Moreover, we formulate the ISI index in terms of these matrices.