Algebraic Graph Theory - Himanshu Gupta

Monday, July 17, 2023 11:30 am - 11:30 am EDT (GMT -04:00)

Title: On the eigenvalues of the graphs D(5,q)

Speaker: Himanshu Gupta
Affiliation: University of Delaware
Location: Please contact Sabrina Lato for Zoom link

Abstract: In 1995, Lazebnik and Ustimenko introduced the family of q-regular graphs D(k, q), which is defined for any positive integer k and prime power q. The connected components of the graph D(k, q) have provided the best-known general lower bound on the size of a graph for any given order and girth to this day. Furthermore, Ustimenko conjectured that the second largest eigenvalue of D(k, q) is always less than or equal to 2√q, indicating that the graphs D(k, q) are good expanders. In this talk, we will discuss some recent progress on this conjecture. This includes the result that the second largest eigenvalue of D(5, q) is less than or equal to 2√q when q is an odd prime power. This is joint work with Vladislav Taranchuk.