|
Horst Sachs
Horst Sachs (27 March 1927 – 25 April 2016) was 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. Following his retirement in 1992, he was 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.Review by P. Rowlinson (1996), ''Proceedings of the Edinburgh Mathematical Society (Series 2)'' 39: 188–189, . 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 In the math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horst Sachs
Horst Sachs (27 March 1927 – 25 April 2016) was 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. Following his retirement in 1992, he was 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.Review by P. Rowlinson (1996), ''Proceedings of the Edinburgh Mathematical Society (Series 2)'' 39: 188–189, . 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 In the math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bojan Mohar
Bojan Mohar (born September 21, 1956) is a Slovenian and Canadian mathematician, working in graph theory. He is a professor of mathematics at the University of Ljubljana and the holder of a Canada Research Chair in graph theory at Simon Fraser University in Vancouver, British Columbia, Canada.Canada Research Chairs – Chairholders – Bojan Mohar accessed 2011-12-09. Education Mohar received his PhD from the University of Ljubljana in 1986, under the supervision of Tomo Pisanski.Research Mohar's research concerns |
Graph Theorists
Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discrete mathematics * Graph of a function *Graph of a relation *Graph paper *Chart, a means of representing data (also called a graph) Computing * Graph (abstract data type), an abstract data type representing relations or connections *graph (Unix), Unix command-line utility *Conceptual graph, a model for knowledge representation and reasoning Other uses * HMS ''Graph'', a submarine of the UK Royal Navy See also *Complex network *Graf *Graff (other) *Graph database *Grapheme, in linguistics *Graphemics *Graphic (other) *-graphy (suffix from the Greek for "describe," "write" or "draw") *List of information graphics software This is a list of software to create any kind of information graphics: * either includes the ability t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1927 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sachs Subgraph
In graph theory, a Sachs subgraph of a given graph is a subgraph in which all connected components are either single edges or cycles. These subgraphs are named after Horst Sachs, who used them in an expansion of the characteristic polynomial of the adjacency matrix of graphs. A similar expansion using Sachs subgraphs is also possible for permanental polynomials of graphs. Sachs subgraphs and the polynomials calculated with their aid have been applied in chemical graph theory, for instance as part of a test for the existence of non-bonding orbitals in hydrocarbon structures. A spanning Sachs subgraph, also called a -factor, is a Sachs subgraph in which every vertex of the given graph is incident to an edge of the subgraph. The union of two perfect matching In graph theory, a perfect matching in a graph is a matching that covers every vertex of the graph. More formally, given a graph , a perfect matching in is a subset of edge set , such that every vertex in the vertex set ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Graph
In the mathematical discipline of graph theory, the line graph of an undirected graph is another graph that represents the adjacencies between edges of . is constructed in the following way: for each edge in , make a vertex in ; for every two edges in that have a vertex in common, make an edge between their corresponding vertices in . The name line graph comes from a paper by although both and used the construction before this. Other terms used for the line graph include the covering graph, the derivative, the edge-to-vertex dual, the conjugate, the representative graph, and the θ-obrazom, as well as the edge graph, the interchange graph, the adjoint graph, and the derived graph., p. 71. proved that with one exceptional case the structure of a connected graph can be recovered completely from its line graph. Many other properties of line graphs follow by translating the properties of the underlying graph from vertices into edges, and by Whitney's theorem the same t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Characteristic Polynomial
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It has the determinant and the trace of the matrix among its coefficients. The characteristic polynomial of an endomorphism of a finite-dimensional vector space is the characteristic polynomial of the matrix of that endomorphism over any base (that is, the characteristic polynomial does not depend on the choice of a basis). The characteristic equation, also known as the determinantal equation, is the equation obtained by equating the characteristic polynomial to zero. In spectral graph theory, the characteristic polynomial of a graph is the characteristic polynomial of its adjacency matrix. Motivation In linear algebra, eigenvalues and eigenvectors play a fundamental role, since, given a linear transformation, an eigenvector is a vector whose direction is not changed by the transformation, and the corresponding eigenva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Applied Mathematics And Mechanics
The ''Journal of Applied Mathematics and Mechanics'', also known as ''Zeitschrift für Angewandte Mathematik und Mechanik'' or ''ZAMM'' is a monthly peer-reviewed scientific journal dedicated to applied mathematics. It is published by Wiley-VCH on behalf of the Gesellschaft für Angewandte Mathematik und Mechanik. The editor-in-chief is Holm Altenbach (Otto von Guericke University Magdeburg). According to the ''Journal Citation Reports'', the journal has a 2021 impact factor of 1.759. Publication history The journal's first issue appeared in 1921, published by the Verein Deutscher Ingenieure and edited by Richard von Mises. in the |
VEB Deutscher Verlag Der Wissenschaften
(DVW) (English: ''German Publisher of Sciences'') was a scientific publishing house in the former German Democratic Republic (GDR/). Situated in Berlin, DVW was founded as (VEB) on 1 January 1954 as the successor of the main department of "university literature" of the publisher (VWV). During the first ten years, DVW, for the most part, published mathematical and scientific literature aimed at university education. About 780 titles were introduced with a total print run of some 3.7 million books. In 1964, DVW took over parts of the programme of and also published textbooks on topics of philosophy, history and sociology. DVW was among the publishers of the (MSB). Whilst more than a third of the production was distributed into Western foreign countries, the publisher still did not make a profit due to the fixed low book prices, politically motivated so called ' (PAOs) dictated by the East German government. In 1988, with a turnaround of 8.4 million East German mark, DVW los ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Graph Theory
In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix. The adjacency matrix of a simple undirected graph is a real symmetric matrix and is therefore orthogonally diagonalizable; its eigenvalues are real algebraic integers. While the adjacency matrix depends on the vertex labeling, its spectrum is a graph invariant, although not a complete one. Spectral graph theory is also concerned with graph parameters that are defined via multiplicities of eigenvalues of matrices associated to the graph, such as the Colin de Verdière number. Cospectral graphs Two graphs are called cospectral or isospectral if the adjacency matrices of the graphs are isospectral, that is, if the adjacency matrices have equal multisets of eigenvalues. Cospectral graphs need not be isomorphic, but isomorphic graphs a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
