A resistance invariant of special alternating links

Abstract

We introduce a Laplacian trace invariant for special, reduced, alternating diagrams of oriented knots and links and show that it is determined by two consecutive coefficients at an extreme of the Alexander polynomial. The invariant also admits an interpretation as one half of the sum of the directed resistances associated with the normalized balanced Tait-graph Laplacian. Explicit flype-related examples show that the Laplacian characteristic polynomial need not be preserved although the invariant is preserved.