\documentclass[12pt]{article} \usepackage{amsmath,mathrsfs,bbm} \usepackage{amssymb} \textwidth=4.825in \overfullrule=0pt \thispagestyle{empty} \begin{document} \noindent % % {\bf Mikhail Isaev} % % \medskip \noindent % % {\bf Asymptotic Behaviour of the Number of Eulerian Circuits} % % \vskip 5mm \noindent % % % % 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. \end{document} .