Asymptotic behaviour of the number of Eulerian circuits. (English)
Electron. J. Comb. 18, No. 1, Research Paper P219, 35 p., electronic only (2011).
Summary: We determine the asymptotic behaviour of the number of Eulerian circuits in undirected simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). We also prove some new properties of the Laplacian matrix.
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