Robert Wertheimer Frucht (later known as Roberto Frucht) (9 August 1906 – 26 June 1997) was a German-Chilean mathematician; his research specialty was

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

and the symmetries of graphs.

Education and career

In 1908, Frucht's family moved from

Brünn Brno ( , ; german: Brünn ) is a Statutory city (Czech Republic), city in the South Moravian Region of the Czech Republic. Located at the confluence of the Svitava (river), Svitava and Svratka (river), Svratka rivers, Brno has about 380,000 inha ...

Austria-Hungary Austria-Hungary, often referred to as the Austro-Hungarian Empire,, the Dual Monarchy, or Austria, was a constitutional monarchy and great power in Central Europe between 1867 and 1918. It was formed with the Austro-Hungarian Compromise of ...

(now in the

Czech Republic The Czech Republic, or simply Czechia, is a landlocked country in Central Europe. Historically known as Bohemia, it is bordered by Austria to the south, Germany to the west, Poland to the northeast, and Slovakia to the southeast. The ...

), where he was born, to

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...

. Frucht entered the

University of Berlin Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...

in 1924 with an interest in

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

, but switched to

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

under the influence of his

doctoral advisor A doctoral advisor (also dissertation director, dissertation advisor; or doctoral supervisor) is a member of a university faculty whose role is to guide graduate students who are candidates for a doctorate, helping them select coursework, as well ...

Issai Schur Issai Schur (10 January 1875 – 10 January 1941) was a Russian mathematician who worked in Germany for most of his life. He studied at the University of Berlin. He obtained his doctorate in 1901, became lecturer in 1903 and, after a stay at the ...

; he received his Ph.D. in 1931. Unable to find academic employment in Germany due to his

Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...

descent, he became an

actuary An actuary is a business professional who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science. These risks can affect both sides of the balance sheet and require asset man ...

Trieste Trieste ( , ; sl, Trst ; german: Triest ) is a city and seaport in northeastern Italy. It is the capital city, and largest city, of the autonomous region of Friuli Venezia Giulia, one of two autonomous regions which are not subdivided into provi ...

, but left Italy in 1938 because of the racial laws that came into effect at that time. He moved to

Argentina Argentina (), officially the Argentine Republic ( es, link=no, República Argentina), is a country in the southern half of South America. Argentina covers an area of , making it the second-largest country in South America after Brazil, th ...

, 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 The Federico Santa María Technical University ( es, Universidad Técnica Federico Santa María, UTFSM, or simply Santa Maria University) is a Chilean university member of the Rector's Council, founded in 1926 in Valparaíso, Chile. The univers ...

in Valparaiso,

Chile Chile, officially the Republic of Chile, is a country in the western part of South America. It is the southernmost country in the world, and the closest to Antarctica, occupying a long and narrow strip of land between the Andes to the east a ...

, 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.

Contributions

Frucht is known for

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. More strongly, for any fini ...

, the result that every group can be realized as the group of

symmetries Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...

of an

undirected graph In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called '' v ...

, and for the

Frucht graph In the mathematical field of graph theory, the Frucht graph is a cubic graph with 12 vertices, 18 edges, and no nontrivial symmetries. It was first described by Robert Frucht in 1939. The Frucht graph is a pancyclic, Halin graph with chromati ...

, one of the five smallest

cubic graph In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs. A bicubic graph is a cubic bipa ...

s without any nontrivial symmetries.

LCF notation In the mathematical field of graph theory, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert Frucht, for the representation of cubic graphs that contain a Hamiltonian cycle. The cycle ...

, a method for describing cubic

Hamiltonian graph In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex ...

s, was named for the initials of

Joshua Lederberg Joshua () or Yehoshua ( ''Yəhōšuaʿ'', Tiberian: ''Yŏhōšuaʿ,'' lit. 'Yahweh is salvation') ''Yēšūaʿ''; syr, ܝܫܘܥ ܒܪ ܢܘܢ ''Yəšūʿ bar Nōn''; el, Ἰησοῦς, ar , يُوشَعُ ٱبْنُ نُونٍ '' Yūšaʿ ...

H. S. M. Coxeter Harold Scott MacDonald "Donald" Coxeter, (9 February 1907 – 31 March 2003) was a British and later also Canadian geometer. He is regarded as one of the greatest geometers of the 20th century. Biography Coxeter was born in Kensington t ...

, and Frucht, its key developers. With Coxeter and David L. Powers, Frucht was coauthor of a book on zero-symmetric graphs, the cubic graphs that have exactly one symmetry taking each vertex to each other vertex.

Recognition

Frucht was elected to the Chilean Academy of Sciences as a corresponding member in 1979. A special issue of the ''

Journal of Graph Theory The ''Journal of Graph Theory'' is a peer-reviewed mathematics journal specializing in graph theory and related areas, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The s ...

'' 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.

Selected publications

References

{{DEFAULTSORT:Frucht, Robert 1906 births 1997 deaths Scientists from Berlin People from the Margraviate of Moravia Czech Jews Jewish emigrants from Nazi Germany to Chile 20th-century Chilean mathematicians Graph theorists 20th-century German mathematicians Humboldt University of Berlin alumni