The Alexander Polynomial of Planar Even Valence Graphs

@inproceedings{Murasugi2001TheAP,
title={The Alexander Polynomial of Planar Even Valence Graphs},
author={Kunio Murasugi and Alexander Stoimenow},
year={2001}
}

We show how the Alexander/Conway link polynomial occurs in the context of planar even valence graphs, refining the notion of the number of their spanning trees. 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.