Intermediate
Discrete Mathematics & Math
Q50 / 100
What is Kirchhoff's matrix tree theorem?
Correct! Well done.
Incorrect.
The correct answer is B) The number of spanning trees of a graph G equals any cofactor of the Laplacian matrix L = D - A
B
Correct Answer
The number of spanning trees of a graph G equals any cofactor of the Laplacian matrix L = D - A
Explanation
The Laplacian L has degree matrix D minus adjacency matrix A. Any cofactor of L (determinant of (n-1)×(n-1) submatrix) counts spanning trees. Generalizes Cayley's formula for non-complete graphs.
Progress
50/100