**Roberto Frucht** was a Czech-born mathematician who moved to Chile before the Second World War. He worked in group theory and graph theory.

- When Frucht entered the school the director was Adolf Busse (1856-1942).
- Frucht passed his matriculation examination at Michaelmas 1924 (in September) giving him the right to study at university.
- The theory of relativity and quantum mechanics were, at this time, changing the nature of physics and the young Frucht wanted to be part of this revolution but was unsure whether reading mathematics or physics at university would be the right route to follow.
- Taking courses in mathematics, physics and philosophy during his first few semesters at university convinced Frucht that physics was not for him.
- Frucht quickly realised that he lacked the necessary manual dexterity to be a successful experimental physicist so came more and more to concentrate on mathematics.
- Schur was happy to be Frucht's thesis advisor but only on the condition that he undertook research on group theory.
- In his thesis Frucht lists all the professors who taught him at the University of Berlin: Ludwig Bieberbach, Georg Feigl, Heinz Hopf, Wolfgang Köhler (1887-1967), Karl Löwner, Richard von Mises, Walther Nerst (1864-1941), Max Planck, Alfred Pringsheim, Emil Rupp (1898-1979), Erhard Schmidt, Wilhelm Schlenk (1879-1943), Erwin Schrödinger, Issai Schur, Edward Spranger (1882-1963), Arthur Wehnelt (1871-1944) and Max Wertheimer (1880-1943).
- Despite Frucht saying that this was a boring period for his mathematics, he did publish a number of papers.
- One of the questions that Dénes König posed in this book concerned automorphisms of graphs and, after working on the problem for some time, Frucht was able to solve it.
- In it Frucht proved what today is known as 'Frucht's Theorem', namely that given any finite group AAA there exists a graph GGG whose automorphism group is isomorphic to AAA.
- Also in this paper, Frucht gives a 3-regular graph with 12 vertices and 18 edges which has a trivial automorphism group.
- This graph is today known as the 'Frucht graph'.
- Frucht managed to find work as an actuary at an insurance company in Buenos Aires.
- Frucht and Breusch were about the same age and they became friends at that time.
- After taking up the position at the University Santa Maria in Valparaiso, Frucht published articles on group theory, on graph theory and on other mathematical topics.
- Many of Frucht's graph theory papers involve both groups and graphs such as On the groups of repeated graphs (1949), Graphs of degree three with a given abstract group (1949) and (with Frank Harary) On the corona of two graphs (1970).
- Examples of Frucht's graph theory papers are A one-regular graph of degree three (1952), How to describe a graph (1970), and A canonical representation of trivalent Hamiltonian graphs (1970).
- In 1970 Frucht retired and was made professor emeritus.
- Frucht remained faithful to Chile although across the country as a whole, mathematical research almost stopped completely.
- Frucht however, continued to undertake research and publish his results although, we note, from around that time his publications are in English rather than Spanish.
- We began to correspond with Leech in Scotland, Coxeter in Canada, Frucht in Chile and Abe Sinkov in Arizona who were all working on the problem.
- In 1978 Coxeter and Frucht presented a paper A new trivalent symmetrical graph with 110 vertices to the 'Second International Conference on Combinatorial Mathematics' held in New York.
- Coxeter, Frucht and Powers published a book Zero-symmetric graphs in 1981.
- his nickname "Toro Frucht" was because he made a kind of guttural sound while he was searching in his mind for the correct word in Spanish to answer questions from his students.
- Roberto and Mercedes usually conversed in a mixture of Castilian, Italian, French and German but because of my presence, they added English to the list that day.
- Frucht received many honours.
- Frucht was elected president of the Society.

Born 9 August 1906, Brünn, Austria-Hungary, now Brno, Czech Republic. Died 26 June 1997, Valparaiso, Chile.

View full biography at MacTutor

Group Theory, Origin Czech Republic

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive