On Schwenk-like Formulas for \(Q\)-Characteristic Polynomials of Graphs

Abstract

Two Schwenk-like formulas about the signless Laplacian matrix of a graph are given, and thus it gives new tools for computing \(Q\)-
characteristic polynomials of graphs directly. As an application, we give the \(Q\)-characteristic polynomial of lollipop graphs and reprove the known result that no two non-isomorphic lollipop graphs are \(Q\)-cospectral by a simple manner.