Robert Frucht
Encyclopedia
Robert Wertheimer Frucht (later known as Roberto Frucht) (August 9, 1906 – June 26, 1997) was a German
-Chile
an mathematician
; his research specialty was graph theory
and the symmetries of graphs
.
In 1908, Frucht's family moved from Brno
(now in the Czech Republic
), where he was born, to Berlin
. Frucht entered the University of Berlin in 1924 with an interest in differential geometry, but switched to group theory
under the influence of his doctoral advisor
, Issai Schur
; he received his Ph.D. in 1931. Unable to find academic employment in Germany due to his Czech citizenship, he became an actuary
in Trieste
, but left Italy in 1938 because of the racial laws that came into effect at that time. He moved to Argentina
, where relatives of his wife lived, and attempted to move from there to the United States, but his employment outside academia prevented him from obtaining the necessary visa. At the same time Robert Breusch
, another German mathematician who had been working in Chile for three years but was leaving for the U.S., invited Frucht to fill his position at Federico Santa María Technical University in Valparaiso
, Chile
, where Frucht found an academic home beginning in 1939. At Santa María, Frucht became dean of the faculty of mathematics and physics from 1948 to 1968, and retired to become an emeritus professor in 1970.
Frucht is known for Frucht's theorem
, the result that every group can be realized as the group of symmetries
of an undirected graph, and for the Frucht graph
, one of the two smallest cubic graphs without any nontrivial symmetries. LCF notation
, a method for describing cubic Hamiltonian graphs, was named for the initials of Joshua Lederberg
, H. S. M. Coxeter, and Frucht, its key developers.
Frucht was elected to the Chilean Academy of Sciences as a corresponding member in 1979.
A special issue of the Journal of Graph Theory
was published in Frucht's honor in 1982, and another special issue of the journal Scientia, Series A (the journal of the mathematics department of Federico Santa María Technical University) was published in honor of his 80th birthday in 1986.
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
-Chile
Chile
Chile ,officially the Republic of Chile , is a country in South America occupying a long, narrow coastal strip between the Andes mountains to the east and the Pacific Ocean to the west. It borders Peru to the north, Bolivia to the northeast, Argentina to the east, and the Drake Passage in the far...
an 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....
; his research specialty was 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...
and the symmetries of graphs
Graph automorphism
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the edge–vertex connectivity....
.
Brno
Brno by population and area is the second largest city in the Czech Republic, the largest Moravian city, and the historical capital city of the Margraviate of Moravia. Brno is the administrative centre of the South Moravian Region where it forms a separate district Brno-City District...
(now in the Czech Republic
Czech Republic
The Czech Republic is a landlocked country in Central Europe. The country is bordered by Poland to the northeast, Slovakia to the east, Austria to the south, and Germany to the west and northwest....
), where he was born, to Berlin
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
. Frucht entered the University of Berlin in 1924 with an interest in differential geometry, but switched to group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
under the influence of his doctoral advisor
Doctoral advisor
A doctoral advisor is an advanced member of a university faculty whose role is to guide a graduate student who is a candidate for a doctorate degree, helping them select coursework, as well as shaping, refining and directing the students' choice of sub-discipline...
, Issai Schur
Issai Schur
Issai Schur was a mathematician who worked in Germany for most of his life. He studied at Berlin...
; he received his Ph.D. in 1931. Unable to find academic employment in Germany due to his Czech citizenship, he became an actuary
Actuary
An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....
in Trieste
Trieste
Trieste is a city and seaport in northeastern Italy. It is situated towards the end of a narrow strip of land lying between the Adriatic Sea and Italy's border with Slovenia, which lies almost immediately south and east of the city...
, but left Italy in 1938 because of the racial laws that came into effect at that time. He moved to Argentina
Argentina
Argentina , officially the Argentine Republic , is the second largest country in South America by land area, after Brazil. It is constituted as a federation of 23 provinces and an autonomous city, Buenos Aires...
, where relatives of his wife lived, and attempted to move from there to the United States, but his employment outside academia prevented him from obtaining the necessary visa. At the same time Robert Breusch
Robert Breusch
Robert Hermann Breusch was a German-American number theorist, the William J. Walker Professor of Mathematics at Amherst College....
, another German mathematician who had been working in Chile for three years but was leaving for the U.S., invited Frucht to fill his position at Federico Santa María Technical University in Valparaiso
Valparaíso
Valparaíso is a city and commune of Chile, center of its third largest conurbation and one of the country's most important seaports and an increasing cultural center in the Southwest Pacific hemisphere. The city is the capital of the Valparaíso Province and the Valparaíso Region...
, Chile
Chile
Chile ,officially the Republic of Chile , is a country in South America occupying a long, narrow coastal strip between the Andes mountains to the east and the Pacific Ocean to the west. It borders Peru to the north, Bolivia to the northeast, Argentina to the east, and the Drake Passage in the far...
, where Frucht found an academic home beginning in 1939. At Santa María, Frucht became dean of the faculty of mathematics and physics from 1948 to 1968, and retired to become an emeritus professor in 1970.
Frucht is known for Frucht's theorem
Frucht's theorem
Frucht's theorem is a theorem in algebraic graph theory conjectured by Dénes Kőnig in 1936 and proved by Robert Frucht in 1939. It states that every finite group is the group of symmetries of a finite undirected graph...
, the result that every group can be realized as the group of symmetries
Graph automorphism
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the edge–vertex connectivity....
of an undirected graph, and for the Frucht graph
Frucht graph
In the mathematical field of graph theory, the Frucht graph is a 3-regular graph with 12 vertices, 18 edges, and no nontrivial symmetries. It was first described by Robert Frucht in 1939....
, one of the two smallest cubic graphs without any nontrivial symmetries. LCF notation
LCF notation
In combinatorial mathematics, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by Coxeter and Frucht, for the representation of cubic graphs that are Hamiltonian. Since the graphs are Hamiltonian, the vertices can be arranged in a cycle, which accounts for two edges...
, a method for describing cubic Hamiltonian graphs, was named for the initials of Joshua Lederberg
Joshua Lederberg
Joshua Lederberg ForMemRS was an American molecular biologist known for his work in microbial genetics, artificial intelligence, and the United States space program. He was just 33 years old when he won the 1958 Nobel Prize in Physiology or Medicine for discovering that bacteria can mate and...
, H. S. M. Coxeter, and Frucht, its key developers.
Frucht was elected to the Chilean Academy of Sciences as a corresponding member in 1979.
A special issue of the Journal of Graph Theory
Journal of Graph Theory
The Journal of Graph Theory is a mathematics journal specializing in graph theory and related areas, such as other branches of combinatorics and the interaction of graph theory with other mathematical sciences...
was published in Frucht's honor in 1982, and another special issue of the journal Scientia, Series A (the journal of the mathematics department of Federico Santa María Technical University) was published in honor of his 80th birthday in 1986.