Horst Sachs
Encyclopedia
Horst Sachs is a German
mathematician
, an expert in graph theory
, a recipient of the Euler Medal
(2000).
He earned the degree of Doctor of Science
(Dr. rer. nat.) from the Martin-Luther-Universität Halle-Wittenberg in 1958. As of 2010, he is professor emeritus at the Institute of Mathematics of the Technische Universität Ilmenau
.
His encyclopedic book in spectral graph theory
, Spectra of Graphs. Theory and Applications (with Dragos Cvetković and Michael Doob) has several editions and was translated in several languages.
Two theorems in graph theory bear his name. One of them relates the coefficients of the characteristic polynomial
of a graph to certain structural features of the graph. Another one is a simple relation between the characteristic polynomials of a graph and its line graph
.
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, an expert in graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, a recipient of the Euler Medal
Euler Medal
The Euler Medal, named after the 18th century mathematician Leonhard Euler, is an honor awarded annually by the Institute of Combinatorics and its Applications to a member with a distinguished lifetime contribution to combinatorial research who are still active in research.-Laureates:* 2008: Gabor...
(2000).
He earned the degree of Doctor of Science
Doctor of Science
Doctor of Science , usually abbreviated Sc.D., D.Sc., S.D. or Dr.Sc., is an academic research degree awarded in a number of countries throughout the world. In some countries Doctor of Science is the name used for the standard doctorate in the sciences, elsewhere the Sc.D...
(Dr. rer. nat.) from the Martin-Luther-Universität Halle-Wittenberg in 1958. As of 2010, he is professor emeritus at the Institute of Mathematics of the Technische Universität Ilmenau
Technische Universität Ilmenau
The Ilmenau University of Technology is the technical university of Thuringia and located in Ilmenau Germany...
.
His encyclopedic book in spectral graph theory
Spectral graph theory
In mathematics, spectral graph theory is the study of properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated to the graph, such as its adjacency matrix or Laplacian matrix....
, Spectra of Graphs. Theory and Applications (with Dragos Cvetković and Michael Doob) has several editions and was translated in several languages.
Two theorems in graph theory bear his name. One of them relates the coefficients of the characteristic polynomial
Characteristic polynomial
In linear algebra, one associates a polynomial to every square matrix: its characteristic polynomial. This polynomial encodes several important properties of the matrix, most notably its eigenvalues, its determinant and its trace....
of a graph to certain structural features of the graph. Another one is a simple relation between the characteristic polynomials of a graph and its line graph
Line graph
In graph theory, the line graph L of undirected graph G is another graph L that represents the adjacencies between edges of G...
.