Asymptotic behavior of the number of Eulerian orientations of graphs

M. I. Isaev

doi:10.1134/S0001434613050210

Asymptotic behavior of the number of Eulerian orientations of graphs

M. I. Isaev

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

The class of simple graphs with large algebraic connectivity (the second minimal eigenvalue of the Laplacian matrix) is considered. For graphs of this class, the asymptotic behavior of the number of Eulerian orientations is obtained. New properties of the Laplacian matrix are established, as well as an estimate of the conditioning of matrices with asymptotic diagonal dominance is obtained.

Original language	English
Pages (from-to)	816-829
Number of pages	14
Journal	Mathematical Notes
Volume	93
Issue number	5-6
DOIs	https://doi.org/10.1134/S0001434613050210
Publication status	Published - 2013
Externally published	Yes

Keywords

algebraic connectivity
conditioning of a matrix
Eulerian orientation of a graph
Laplacian matrix
matrix with diagonal dominance
simple graph
spanning tree

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10.1134/S0001434613050210

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abstract = "The class of simple graphs with large algebraic connectivity (the second minimal eigenvalue of the Laplacian matrix) is considered. For graphs of this class, the asymptotic behavior of the number of Eulerian orientations is obtained. New properties of the Laplacian matrix are established, as well as an estimate of the conditioning of matrices with asymptotic diagonal dominance is obtained.",

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AB - The class of simple graphs with large algebraic connectivity (the second minimal eigenvalue of the Laplacian matrix) is considered. For graphs of this class, the asymptotic behavior of the number of Eulerian orientations is obtained. New properties of the Laplacian matrix are established, as well as an estimate of the conditioning of matrices with asymptotic diagonal dominance is obtained.

KW - algebraic connectivity

KW - conditioning of a matrix

KW - Eulerian orientation of a graph

KW - Laplacian matrix

KW - matrix with diagonal dominance

KW - simple graph

KW - spanning tree

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Asymptotic behavior of the number of Eulerian orientations of graphs

Abstract

Keywords

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