Research

Most of my research is on classes of bipartite graphs, especially distance-biregular graphs. From an algebraic perspective, distance-biregular graphs can be seen as a generalization of bipartite distance-regular graphs, with similarly nice algebraic and structural properties. Distance-biregular graphs also arise as extremal examples of graphs with certain structural or spectral properties, or from incidence structures in design theory and finite geometry. More recently, I have also worked on an extension of Cayley graphs to a bipartite context.

I am also interested in poset saturation, orthogonal polynomials and quantum walks.

Papers

• Cayley Incidence Graphs
  Joint work with Arnbjörg Soffía Árnadóttir, Alexey Gordeev, Sabrina Lato, Tovohery Randrianarisoa, Joannes Vermant. Preprint available.

• P-Polynomial and Bipartite Coherent Configurations
  Sabrina Lato, "P-Polynomial and Bipartite Coherent Configurations." Linear Algebra and Applications 708 (2025) 12-41.

• Polynomial Characterizations of Distance-Biregular Graphs
  Sabrina Lato, "Polynomial Characterizations of Distance-Biregular Graphs." Journal of Graph Theory (2025).

• A Spectral Moore Bound for Bipartite Semiregular Graphs
  Sabrina Lato, "A Spectral Moore Bound for Bipartite Semiregular Graphs." SIAM Journal on Discrete Math 37.1 (2023) 315-331.

• Perfect State Transfer on Oriented Graphs
  Chris Godsil and Sabrina Lato, “Perfect State Transfer on Oriented Graphs.” Linear Algebra and Applications 604 (2020) 278-292.

Theses

• Distance-Biregular Graphs and Orthogonal Polynomials
  PhD thesis

• Quantum Walks on Oriented Graphs
  Master's thesis

Talks

• New Characterizations of Distance-Biregular Graphs (on Youtube)

• A Spectral Moore Bound for Bipartite Semiregular Graphs (on Youtube)

• Monogamy Violations in Perfect State Transfer (on Youtube)