The characteristic polynomial of generalized lollipop graphs

A generalized lollipop graph is formed by connecting a tree and a threshold graph with an edge. Motivated by a sequence of algorithms that compute the characteristic polynomial of some classes of graphs, we present an algorithm for computing the characteristic polynomial of generalized lollipop graph with relation to signless Laplacian matrix Q. As application, we show how to construct graphs having Q-cospectral mate.