Mathematics – Combinatorics
Scientific paper
2011-10-12
Mathematics
Combinatorics
arXiv admin note: text overlap with arXiv:1104.3046
Scientific paper
We consider the class of simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). For this class of graphs we determine the asymptotic behavior of the number of Eulerian orientations. In addition, we establish some new properties of the Laplacian matrix, as well as an estimate of a conditionality of matrices with the asymptotic diagonal predominance
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