| In this thesis, we investigate the independence polynomial of a simple graph G. In addition to giving several tools for computing these polynomials and giving closed-form representations of these polynomials for common classes of graphs, we prove two results concerning the roots of independence polynomials. The first result gives us the unique root of smallest modulus of the independence polynomial of a graph. The second result tells us that all the roots of the independence polynomial of a claw-free graph fall on the real line. |
