Skew characteristic polynomial of graphs and embedded graphs (Q6590895)

From the authors' abstract: ``We introduce a new one-variable polynomial invariant of graphs, which we call the skew characteristic polynomial. For an oriented simple graph, this is just the characteristic polynomial of its anti-symmetric adjacency matrix. For non-oriented simple graphs the definition is different, but for a certain class of graphs (namely, for intersection graphs of chord diagrams), it gives the same answer if we endow such a graph with an orientation induced by the chord diagram.\N\NWe prove that this invariant satisfies Vassiliev's 4-term relations and determines therefore a finite type knot invariant.'' \N\N``We also provide a two-variable extension of the skew characteristic polynomial to embedded graphs and delta-matroids. The 4-term relations for the extended polynomial prove that it determines a finite type invariant for multi-component links.''