Yousef Alavi (March 19, 1928 – May 21, 2013) was an Iranian-American mathematician, based at Western Michigan University (WMU), who specialized in graph theory. He received his PhD from Michigan State University in 1958, and his career at WMU lasted until 1996. Alavi was a frequent collaborator with Don R. Lick and Jiuqiang Liu (both of Eastern Michigan University) as well as with Paul Erdős,<!-- MathSciNet collaboration data --> and in 1987, the Michigan Section of the Mathematical Association of America (MAA) awarded him its first annual Distinguished Service Award.
Early life and education (1928–1958)
Alavi was born in the city of Ahvaz in Pahlavi Iran in 1928. There, he earned a bachelor's degree in electrical engineering from Michigan State University in 1953, a master's in math from the same school in 1955, and a PhD in 1958. he chaired the department from 1989 to 1992.
Alavi was known for complaining that "this is highly irregular!" He was also a frequent host for Erdős on his visits to Western Michigan. On one of these visits, these two things came together: he made his usual complaint at a time when Erdős and Ronald Graham were present. This sparked a discussion on what it might mean for a graph to be highly irregular, kicking off a line of joint research on highly irregular graphs through which Alavi obtained Erdős number one.
In 1987, he received the first Distinguished Service Award of the Michigan Section of the MAA due to his 30 years of service to the section; at that time, the Michigan House and Senate issued a special resolution honoring him.
Research
In 1987, Alavi, Erdős, Paresh J. Malde, and Allen J. Schwenk studied the vertex independence sequence <math>a_1, \dots, a_m</math> of an undirected graph where m is the maximal order of any independent set, where <math>a_i</math> denotes the number of independent sets on exactly i vertices. By taking the join of several complete graphs, they were able to show that this sequence can realize any possible permutation.
In 1991, Alavi, Erdős, Mehdi Behzad, and Don R. Lick introduced the notion of the double vertex graph of any graph. Further research involving Alavi, Lick, and Jiuqiang Liu in 1993 and 1994 eventually led to a classification of which Hamiltonian graphs also have Hamiltonian double vertex graphs. He was remembered for possessing "great energy", "kindness", and "good humor". his health had been worsening for several months prior. Speakers included Fan Chung and Ronald Graham, both of the University of California, San Diego.