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.