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GraphTheory

  

GraphPolynomial

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

GraphPolynomial(G,x)

Parameters

G

-

undirected unweighted graph

x

-

name or list(algebraic)

Description

• 

The GraphPolynomial command returns a polynomial in the variables x1,...,xn when x is a symbol and G is a graph with n vertices. The polynomial consists only of linear factors of the form (xj-xk) where j and k represent adjacent vertices.

• 

If x is a list of algebraic expressions whose length is equal to the number of vertices of G, the polynomial is formed using linear factors of the form (xj-xk) where j and k represent adjacent vertices.

Examples

withGraphTheory:

G ≔ Graph1,2,3,4,5,6,4,5,3,4,4,6,5,6,3,5,1,4,2,6:

GraphPolynomialG,x

x1x4x2x6x3x4x3x5x4x5x4x6x5x6

(1)

GraphPolynomialCycleGraph4,x,y,z,w

xyxwyzzw

(2)

References

  

Noga Alon and Michael Tarsi, "A note on graph colorings and graph polynomials", J. Combin. Theory Ser. B 70 (1997), no. 1, 197–201, doi: 10.1006/jctb.1997.1753

Compatibility

• 

The GraphTheory[GraphPolynomial] command was updated in Maple 2019.

See Also

Neighbors

SpanningPolynomial