# Ramanujan Graphs (XI)

*Discrete Structures and Algorithms (Reading Group)*

*by Sanming Zhou*

*Institution:*The University of Melbourne

*Date: Wed 17th April 2013*

*Time: 11:00 AM*

*Location: Room 107, Richard Berry*

*Abstract*: We will first discuss a construction of an irreducible representation of a finite 2-transitive group. Using this we will then prove an old result due to Frobenius which says that for any prime $q \ge 5$ the degree of any nontrivial irreducible representation of $PSL_{2}(q)$ is at least $(q-1)/2$. This result will be used in Chapter 4 to prove that any nontrivial eigenvalue of $X^{p, q}$ has multiplicity at least $(q-1)/2$.