arXiv subjects

V. A. Buslov

Publications and source records attributed to V. A. Buslov.

5 recordsLinked to original sources

arXiv2025

Splitting a graph by a given partition of the set of vertices based on the minimum weight of the induced trees

A method for considering a weighted directed graph with an accuracy of up to a given partition of the set of vertices is proposed. The resulting digraph (the splitting graph) does not contain arcs inside each partition element, and the arcs between the partition atoms are calculated in a special way taking into account the arcs of the original directed graph inside the atoms. This accounting is based on minimal trees defined on atoms. A study was made of what information about the original digraph is preserved in its splitting.

math.CO↗

arXiv2008

On the Minimum Spanning Tree for Directed Graphs with Potential Weights

In general the problem of finding a miminum spanning tree for a weighted directed graph is difficult but solvable. There are a lot of differences between problems for directed and undirected graphs, therefore the algorithms for undirected graphs cannot usually be applied to the directed case. In this paper we examine the kind of weights such that the problems are equivalent and a minimum spanning tree of a directed graph may be found by a simple algorithm for an undirected graph.

cs.DM↗

arXiv2001

Quantum Evolution Supergenerator of Superparamagnetic System in Discrete Orientation Model

The supergenerator of superparamagnetic system quantum evolution is investigated in discrete orientation model (DOM). It is shown that the generator is J-self-adjoint one at the case of potential drift field agreed upon magnetic anisotropy of the sample investigated. Perturbation theory is used for spectral analysis. The qualitative dependence of resonance absorption spectrum on the relation between quantum and stochastic parameters is demonstrated.

physics.atm-clus↗

arXiv2000

Application of Tree-like Structure of Graph to Matrix Analysis

Formulas for matrix determinants, algebraic adjunctions, characteristic polynomial coefficients, components of eigenvectors are obtained in the form of signless sums of matrix elements products taking by special graphs. Signless formulas are very important for singular and stochastic problems. They are also useful for spectral analysis of large very sparse matrices.

math.CO↗

arXiv2000

Hierarchy Structure of Graphs and Weighted Condensations

By natural way the hierarchy structure is introduced on directed graphs with weighted adjacencies. Embedded system of algebras of subsets of the set of vertices of such digraph and it's consolidations, which vertices are the elementary sets of corresponding algebra, are constructed. Weights of arcs of consolidated graphs are determined.

math.CO↗