In 1964 he received his master's degree and in 1966 he obtained his Ph.D. from the University of California, Santa Barbara under the supervision of Paul Kelly.
[4] One of his first publications was an article titled Cycles of each length in regular tournaments, which was published in the Canadian Mathematical Bulletin (November, 1967).
[6] In his article titled Isomorphism of circulant graphs and digraphs which was published in Discrete Mathematics (February, 1979).
Brian Alspach coauthored an article with T. D. Parsons titled A construction for vertex –transitive graph published in the Canadian Journal of Mathematics (April, 1982).
With Heather Gavlas Jordon, in 2001, Alspach proved a special case, on the decomposition of complete graphs into cycles that all have the same length.