Asymptotic behaviour of the number of the Eulerian circuits
Mikhail Isaev (CMAP)
TL;DR
This paper investigates the asymptotic number of Eulerian circuits in large undirected graphs with high algebraic connectivity, revealing new properties of the Laplacian matrix.
Contribution
It provides the asymptotic analysis of Eulerian circuits in graphs with large algebraic connectivity and introduces new properties of the Laplacian matrix.
Findings
Asymptotic formula for Eulerian circuits in high-connectivity graphs
New properties of the Laplacian matrix
Insights into the structure of graphs with large algebraic connectivity
Abstract
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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Taxonomy
TopicsGraph theory and applications · Markov Chains and Monte Carlo Methods · Topological and Geometric Data Analysis