Nov 4 2024

Combinatorics and Discrete Probability Seminar: On the eigenvalues of the graphs D(5,q), by Himanshu Gupta

November 4, 2024

3:00 PM - 3:50 PM

Location

1227 SEO

Address

Chicago, IL

Himanshu Gupta (University of Regina): On the eigenvalues of the graphs D(5,q)

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 almost Ramanujan graphs. 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.

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Contact

Lev Reyzin

Date posted

Nov 4, 2024

Date updated

Nov 4, 2024

Speakers