Horst Sachs

Horst Sachs ( born March 27, 1927 in Magdeburg ) is a German mathematician who is mainly concerned with graph theory.

Life

Sachs was founded in 1958 at the Martin -Luther- University Halle- Wittenberg Herbert Grötzsch doctorate ( Contributions to the Theory of certain isoperimetric problems). He was at the Ilmenau University of Technology, where he is now an emeritus professor since 1963.

Sachs is best known for his contributions to the theory of spectra of graphs on which he wrote a monograph with others. This theory considers different one graph associated matrices ( such as the adjacency matrix ) and examines how reflected statements about the structure of the graph in the properties of the associated matrices ( eigenvalues ​​, eigenvectors, characteristic polynomial ). One chapter of his monograph explains the roots of this theory in applications in quantum chemistry and performs physical applications ( vibration spectrum of a membrane) from. Sachs also dealt with applications of graph theory in chemistry and the history of graph theory. Sachs in 1986 they gave the book theory of finite and infinite graphs of Dénes König in Teubner out again.

Different sets are named after him, including the set of Sachs, which connects the coefficients of the characteristic polynomial of a directed graph with its structural composition of his circle - subgraph:

A is a square matrix, and P (A) the characteristic polynomial of coefficients ( i = 1, ..., n). A is interpreted as the adjacency matrix of a directed graph ( digraph ). Then by the theorem of Sachs ( Koeffiziententheorem for digraphs ):

Here is the set of linear directed subgraphs of the graph with exactly i nodes. is the number of components of L, that is, the cycles of which it is composed.

In 2000 he was awarded the Euler Medal with Richard A. Brualdi. He was chairman of the Mathematical Society of the GDR.

Writings

  • With Dragos Cvetkovic, Michael Doob Spectra of Graphs. Theory and Applications, VEB German Academic Publishers, Academic Press 1980, 2nd edition 1982, 3rd edition, Johann Ambrosius Barth, Heidelberg 1995 ( in 1984 translated into Russian )
  • Publisher Graphs, hyper graphs and applications ( Conference Eyba October 1984), Teubner 1985
  • Publisher (on behalf of the Mathematical Society of the GDR ) The development of mathematics in the GDR. On the 25th anniversary of the GDR, German Academic Publishers, Berlin 1974
  • Introduction to the theory of finite graphs, Hanser in 1971 and in two-volume edition in 1970 Teubner, 1972
  • Publisher with Heinz -Jürgen Voss and Hans Joachim Walther: Contributions to Graph Theory ( Internat. Colloquium Manebach May 1967 ), Teubner 1968
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