On the characteristic polynomial of homeomorphic images of a graph Original Research Article

The characteristic polynomial of a homeomorphic image H(G) of an arbitrary graph G is expressed in terms of simpler characteristic polynomials. This is applied to obtain the characteristic polynomials of various known families of graphs, including the family of theta graphs, H(K2, 3). An improvement of the Chartrand-Harary theorem, which characterises outerplanar graphs and in which the theta graphs appear is presented here.