The class of simple graphs with large algebraic connectivity (the second minimal eigenvalue of the Laplacian matrix) is considered. For graphs of this class, the asymptotic behavior of the number of Eulerian orientations is obtained. New properties of the Laplacian matrix are established, as well as an estimate of the conditioning of matrices with asymptotic diagonal dominance is obtained.
- algebraic connectivity
- conditioning of a matrix
- Eulerian orientation of a graph
- Laplacian matrix
- matrix with diagonal dominance
- simple graph
- spanning tree