Dichroic Polynomial
A Polynomial 
in two variables for abstract Graphs. A Graph with one Vertex has 
. Adding a Vertex notattached by any Edges multiplies the 
by 
. Picking a particular Edge ofa Graph 
, the Polynomial for is defined by adding the Polynomial ofthe Graph with that Edge deleted to 
times the Polynomialof the graph with that Edge collapsed to a point. Setting 
gives the number of distinctVertex colorings of the Graph. The dichroic Polynomial ofa Planar Graph can be expressed as the Square Bracket Polynomial of the corresponding Alternating Linkby
where
is the number of Vertices in . Dichroic Polynomials for some simpleGraphs are |  |  | |
 | |  | |
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References
Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 231-235, 1994.
- Bullet Nose
- Bumping Algorithm
- Bundle
- Burau Representation
- Burkhardt Quartic
- Burnside Problem
- Burnside's Conjecture
- Burnside's Lemma
- Busemann-Petty Problem
- Busy Beaver
- Small Multiple Method
- Small Number
- Small Retrosnub Icosicosidodecahedron
- Small Rhombicosidodecahedron
- Small Rhombicuboctahedron
- Small Rhombidodecacron
- Small Rhombidodecahedron
- Small Rhombihexacron
- Small Rhombihexahedron
- Small Snub Icosicosidodecahedron
- Small Stellapentakis Dodecahedron
- Small Stellated Dodecahedron
- Small Stellated Triacontahedron
- Small Stellated Truncated Dodecahedron
- Small Triakis Octahedron