The Alexander Polynomial of Planar Even Valence Graphs

This is a summary of my old paper with Murasugi, where we show, using the Kauffman state model, how the Alexander/Conway link polynomial occurs in the context of planar even valence graphs. Then we apply knot theory to deduce several statements about this graph polynomial, in particular estimates for its coefficients and relations between congruences of the number of vertices and number of spanning trees of the graph.