A new invariant of plane bipartite cubic graphs (Q1197024)

This paper presents a new polynomial invariant of plane bipartite cubic graphs. This invariant is the restriction to plane graphs of a certain invariant of oriented bipartite cubic graphs embedded in 3-space, which corresponds in the case of links to a one-variable specialization of the `homfly' polynomial. Several propositions emphasize a close connection with two other invariants of plane cubic graphs, the number of edge-3-colorings and the flow polynomial evaluated at \(\tau+1\), where \(\tau\) is the golden ratio. In addition to an explicit formula in the case of a series parallel graph, the author provides an explicit expression for the polynomial in terms of edge-3-colorings.