Asymptotic behaviour of the number of the Eulerian circuits
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asymptoticbehaviourcircuitseulerianlaplacianmatrixnumberalgebraic
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We determine the asymptotic behaviour of the number of the 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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