Frank Harary
Encyclopedia
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....
, who specialized 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...
. He was widely recognized as one of the "fathers" of modern graph theory.
Harary was a master of clear exposition and, together with his many doctoral students, he standardized the terminology of graphs. He broadened the reach of this field to include physics, psychology, sociology, and even
anthropology. Gifted with a keen sense of humor, Harary challenged and entertained audiences at all levels of mathematical sophistication. A particular trick he employed was to turn theorems into games - for instance,
students would try to add red edges to a graph on six vertices in order to create a red triangle, while another group of students tried to add edges to create a blue triangle (and each edge of the graph had to be either blue
or red). Because of the simplest case of Ramsey theory
Ramsey theory
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear...
, one team or the other would have to win!
Biography
Frank Harary was born in New York CityNew York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
, the oldest child to a family of Jewish immigrants from Syria
Syria
Syria , officially the Syrian Arab Republic , is a country in Western Asia, bordering Lebanon and the Mediterranean Sea to the West, Turkey to the north, Iraq to the east, Jordan to the south, and Israel to the southwest....
and Palestine
Palestine
Palestine is a conventional name, among others, used to describe the geographic region between the Mediterranean Sea and the Jordan River, and various adjoining lands....
. He earned his Bachelor's and Master's degrees from Brooklyn College
Brooklyn College
Brooklyn College is a senior college of the City University of New York, located in Brooklyn, New York, United States.Established in 1930 by the New York City Board of Higher Education, the College had its beginnings as the Downtown Brooklyn branches of Hunter College and the City College of New...
in 1941 and 1945 respectively and his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
from University of California at Berkeley in 1948. During 1948-1986 he was with the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
. From 1987 he was Professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
(and Distinguished Professor Emeritus) in the Computer Science Department at New Mexico State University
New Mexico State University
New Mexico State University at Las Cruces , is a major land-grant university in Las Cruces, New Mexico, United States...
in Las Cruces
Las Cruces, New Mexico
Las Cruces, also known as "The City of the Crosses", is the county seat of Doña Ana County, New Mexico, United States. The population was 97,618 in 2010 according to the 2010 Census, making it the second largest city in the state....
. He was one of the founders of the Journal of Combinatorial Theory
Journal of Combinatorial Theory
The Journal of Combinatorial Theory, Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. Series A is concerned primarily with structures, designs, and applications of combinatorics. Series B is concerned primarily with...
and 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...
. He died at Memorial Medical Center in Las Cruces, New Mexico
Las Cruces, New Mexico
Las Cruces, also known as "The City of the Crosses", is the county seat of Doña Ana County, New Mexico, United States. The population was 97,618 in 2010 according to the 2010 Census, making it the second largest city in the state....
.
Mathematics
Harary's work in graph theory was diverse. Some topics of great interest to him were:- Graph enumerationGraph enumerationIn combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the graph...
, that is, counting graphs of a specified kind. He coauthored a book on the subject (Harary and Palmer 1973). The main difficulty is that two graphs that are isomorphic should not be counted twice; thus, one has to apply Polya's theory of counting under group action. Harary was an expert in this. - Signed graphs. Harary invented this branch of graph theory, which grew out of a problem of theoretical social psychologySocial psychologySocial psychology is the scientific study of how people's thoughts, feelings, and behaviors are influenced by the actual, imagined, or implied presence of others. By this definition, scientific refers to the empirical method of investigation. The terms thoughts, feelings, and behaviors include all...
investigated by the psychologist Dorwin Cartwright and Harary. - Applications of graph theory in numerous areas, especially to social science. He was co-author of John Wiley's first eBook, Graph Theory and Geography.
Among over 700 scholarly articles Harary wrote, two were co-authored with Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
, giving Harary an Erdős number
Erdos number
The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.The same principle has been proposed for other eminent persons in other fields.- Overview :...
of 1. He lectured extensively and kept alphabetical lists of the cities where he spoke.