Zagreb Spectral Radii of Splitting and Shadow Graphs

The spectral radius [Formula: see text] of graph [Formula: see text] is an essential component that is associated with the eigenvalues of the matrix of graph [Formula: see text] and, chemically, with the intermolecular forces. This graph invariant has many useful applications in computer sciences, networking, and molecular computing. There are numerous variants of the [Formula: see text] attained by substituting another matrix in place of an adjacency matrix. First Zagreb spectral radius, [Formula: see text] is defined as the largest absolute eigenvalue of the first Zagreb matrix and Second Zagreb spectral radius, [Formula: see text] is defined as the largest absolute eigenvalue of the second Zagreb matrix. The major focus of this article is on the [Formula: see text], [Formula: see text] of the generalized shadow and splitting graphs. The only realistic problem in which we are particularly interested in how [Formula: see text] and [Formula: see text] are comparable to [Formula: see text] and [Formula: see text] respectively. We were able to address this challenge by focusing on splitting graphs. We are also interested in how [Formula: see text] and [Formula: see text] are comparable to [Formula: see text] and [Formula: see text] respectively. We were able to address this challenge by focusing on shadow graphs.