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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.
A model describing the interaction of a short oligonucleotide with long polynucleotide matrix has been developed. The model allows to calculate possibilities of oligonucleotide binding with different matrix sites on the basis of thermodynamic parameters of duplex formation. The model has been used for description of messenger RNA interaction with… (More)
We study three mixing properties of a graph: large algebraic connec-tivity, large Cheeger constant (isoperimetric number) and large spectral gap from 1 for the second largest eigenvalue of the transition probability matrix of the random walk on the graph. We prove equivalence of this properties (in some sense). We give estimates for the probability for a… (More)