A polynomial in two variables for abstract graphs. A graph with one graph vertex has . Adding a graph vertex not attached by any graph edges multiplies the by . Picking a particular graph edge of a graph , the polynomial for is defined by adding the polynomial of the graph with that graph edge deleted to times the polynomial of the graph with that graph edge collapsed to a point.
Setting gives the chromatic number of the graph. The dichroic polynomial of a planar graph can be expressed as the square bracket polynomial of the corresponding alternating link by
(1)

where is the number of graph vertices in . Dichroic polynomials for some simple graphs are
(2)
 
(3)
 
(4)
