Enumeration of labeled bicyclic and tricyclic Eulerian graphs

Explicit formulas for the number of labeled bicyclic and tricyclic Eulerian graphs and for the number of labeled tricyclic Eulerian blocks are obtained. Many-vertex asymptotics for these numbers are found.     

Enumeration of labeled geodetic graphs with small cyclomatic number

Explicit expressions for the numbers of labeled geodetic bicyclic, tricyclic, and tetracyclic graphs with a given number of vertices are obtained.     

Enumeration of labeled outerplanar bicyclic and tricyclic graphs

The class of outerplanar graphs is used for testing the average complexity of algorithms on graphs. A random labeled outerplanar graph can be generated by a polynomial algorithm based on the results of an enumeration of such graphs. By a bicyclic (tricyclic) graph we mean a connected graph with cyclomatic number 2 (respectively, 3). We find explicit formulas for the number of labeled connected outerplanar bicyclic and tricyclic graphs with n vertices and also obtain asymptotics for the number of these graphs for large n. Moreover, we obtain explicit formulas for the number of labeled outerplanar bicyclic and tricyclic n-vertex blocks and deduce the corresponding asymptotics for large n.     

On the Enumeration of Labeled Series-Parallel $$k $$ -Cyclic $$2 $$ -Connected Graphs

Journal of Applied and Industrial Mathematics - We deduce an explicit formula for the number of labeled series-parallel $$k $$ -cyclic $$n $$ -vertex $$2 $$ -connected graphs and find the...     

On the Asymptotic Enumeration of Labeled Connected k-Cyclic Graphs without Bridges

Mathematical Notes -     

Enumeration of labeled,connected, homeomorphically irreducible graphs

Translated from Matematicheskie Zametki, Vol. 49, No. 3, pp. 12–22, March, 1991.     

Enumeration of labeled block-cactus graphs

The exact and asymptotic formulas are obtained for the number of block-cactus graphs and Eulerian block-cactus graphs with a given number of vertices.     

A condition for the asymptotic stability of a linear homogeneous system whose principal part is a Jordan matrix

This paper presents an investigation of the asymptotic stability of a linear system of ordinary differential equations in which the principal part is a Jordan matrix with variable coefficients and the perturbation matrix can have an arbitrary structure.Translated from Matematicheskie Zametki, Vol. 8, No. 6, pp. 761–772, December, 1970.The author wishes to thank A. A. Abramov for his interest in this work and for his many useful suggestions.