Title：On the eigenvalues of some algebraically defined graphs : a survey

Abstract：This is a literature review report on the spectrum of some algebraically defined graphs. This family graph giving the best known bounds on extremal problems with forbidden even cycles, and also gives the explicit construction of semisymmetric graphs. Despite this, little is known about the spectrum and expansion properties of these graphs. In 2014, Cioaba et al completely described the spectrum of the Wenger graph. These same authors popularized their research methods in 2017. Then Cao et al. determined the eigenvalues of linear Wenger graphs. In 2017, Moorhouse et al determined the eigenvalue of D(k,q) for k=4 and verified the conjecture of Ustimenko. Recently, Gupta et al verified this conjecture for the case of k = 5, 6. In this survey, we will introduce the research methods in these papers.

Speaker：Fu-Yuan Yang, Moutai Institute. His research interests include Algebra and graph theory. His results published on《Axioms》 and 《Bulletin of the Malaysian Mathematical Sciences Society》.

Date：19:00pm-21:00pm 2022-11-22（Tuesday）.

Tencent Meeting ID： 729 254 127

Organizer：School of Mathematical Science

Students and teachers who are interested in graph theory are welcome.