The Kauffman polynomial of alternating links

Let D be an alternating diagram and ΛD(a, z) ε Z[a ± 1, z ± 1] the regular isotopy invariant of D introduced by L.H. Kauffman. With respect to variable a, the maximal and minimal degrees of ΛD(a, z) are given. Furthermore, it will be shown that the shape of D is strongly reflected in the coefficient polynomials at the maximal and minimal powers of a.