Mathematical Sciences Department Discrete Math Seminar
Monday (March 17) 3:00 pm
Stratton Hall 301
Speaker: Michael D. Barrus, University of Rhode Island
Title: A class of trees determined by their adjacency spectrum
Abstract: How much can the adjacency spectrum be used to identify an unknown graph? It has been conjectured by some that almost every graph has a spectrum unique to itself, but Schwenk (1973) showed that almost every tree shares its adjacency eigenvalues with another tree, and Godsil and McKay (1982) and many others have provided means of constructing pairs of graphs with the same spectrum.
In this talk, based on work done with Emily Barranca (St. Mary's College of Maryland) in her dissertation, we focus on the question for double stars, i.e., trees of diameter at most 3. We verify that many double stars (perhaps almost all) share their spectrum with some other non-tree graph. However, we prove that one type of double star--one formed by subdividing an edge in a star with an even number of leaves--is always uniquely determined by its spectrum.