Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2025 07 07 A spectral analysis of the Schultz index 14982 10.22049/cco.2025.30370.2442 EN Angie L. Galán-Cipagauta Faculty of Mathematics, Universidad Autónoma de Guerrero, Acapulco, México Juan Carlos Hernández-Gómez Faculty of Mathematics, Universidad Autónoma de Guerrero, Acapulco, México Gerardo Reyna-Hernández Faculty of Mathematics, Universidad Autónoma de Guerrero, Acapulco, México Jesús Romero-Valencia Faculty of Mathematics, Universidad Autónoma de Guerrero, Acapulco, México Journal Article 2025 02 20 Topological indices are descriptors that assign a number to each molecular graph, often well correlated to some properties. In particular, the Schultz index has stood out for its high discrimination capacity between different molecular structures, being a key tool in the study of their physicochemical properties. In this paper, we introduce a modification of the classical adjacency matrix making use of the Schultz index, incorporating both the degree of the vertices and the distance between each pair of them. We perform a spectral analysis of this index and identify some of its significant properties. Particularly, we focus on determining upper and lower bounds for the eigenvalues of this matrix, contributing to the understanding of its algebraic structure and its relationship with graph parameters.  Topological indices Schultz index Matrix of a graph Spectrum of a graph https://comb-opt.azaruniv.ac.ir/article_14982_1501aa8c6920209f4ac9d1af173ac93c.pdf