TuttePolynomial
TuttePolynomial[g,{x,y}]
gives the Tutte polynomial of the graph g.
TuttePolynomial[{vw,…},…]
uses rules vw to specify the graph g.
Details
- TuttePolynomial is also known as dichromate polynomial or Tutte–Whitney polynomial.
- TuttePolynomial[g] gives a pure function representation of the Tutte polynomial of g.
- For an undirected graph
with 
vertices and 
connected components, the Tutte polynomial is defined as the sum of 
over all subsets 
of edges of 
. 
is the number of connected components of the graph generated by 
with 
vertices.
Examples
open all close allScope (6)
TuttePolynomial works with undirected graphs:
Applications (6)
Find the number of spanning trees of a complete graph:
Find the number of forests of a cycle graph:
Find the number of spanning subgraphs of a cycle graph:
Find the number of acyclic orientations of a cycle graph:
Find the number of strongly connected orientations of a cycle graph:
Properties & Relations (4)
Isomorphic graphs have the same Tutte polynomial:
The Tutte polynomial of a tree with 
edges is 
:
TuttePolynomial[g,{1,1}] counts the number of spanning trees in the graph:
TuttePolynomial[g,{2,2}] is equal to 2EdgeCount[g]:
Text
Wolfram Research (2014), TuttePolynomial, Wolfram Language function, https://reference.wolfram.com/language/ref/TuttePolynomial.html (updated 2015).
CMS
Wolfram Language. 2014. "TuttePolynomial." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/TuttePolynomial.html.
APA
Wolfram Language. (2014). TuttePolynomial. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TuttePolynomial.html