Knots can be represented by polynomials like the Jones polynomial. Is there a comparable representation for graphs? How does it work for subclasses like planar, k-regular...?
Google doesn't really help here...
Thanks
Knots can be represented by polynomials like the Jones polynomial. Is there a comparable representation for graphs? How does it work for subclasses like planar, k-regular...?
Google doesn't really help here...
Thanks
Also check out the Tutte polynomial. It is actually a generalization of many polynomials in graph theory, including the chromatic polynomial and the Jones polynomial. It's not a "representation" of the graph, per se, but is extensively used.
There are polynomial invariants for graphs. One of them is the characteristic polynomial of the adjacency matrix. This has been studied extensively, for example in connection with the graph isomorphism problem.