If the Tutte polynomial 
of a graph 
is given by 
, then the matrix 
is called the rank matrix of 
.
For example, the Tutte matrix of the Petersen graph is given by
![[0 36 84 75 35 9 1; 36 168 171 65 10 ; 120 240 105 15 ; 180 170 30 ; 170 70 ; 114 12 ; 56 ; 21 ; 6 ; 1 ]](/images/equations/TutteMatrix/NumberedEquation1.svg) |
(Biggs 1973; 1993, p. 103).
Tutte Matrix
See also
Rank Polynomial, Tutte PolynomialExplore with Wolfram|Alpha
References
Biggs, N. L. Algebraic Graph Theory, 2nd ed. Cambridge, England: Cambridge University Press, 1993.Biggs, N. L. "Three Remarkable Graphs." Canad. J. Math. 25, 397-411, 1973.Referenced on Wolfram|Alpha
Tutte MatrixCite this as:
Weisstein, Eric W. "Tutte Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TutteMatrix.html