A class of Ramanujan graphs constructed from nilpotent matrices
by Vernon Oiloom Chan
THESIS
2015
M.Phil. Mathematics
viii, 52 pages : illustrations ; 30 cm
Abstract
Ramanujan graph is one of the central topics of spectral graph theory. A simple
k-regular graph X with second largest eigenvalue μ1 is called Ramanujan if μ1 ≤ 2 √k-1.
Ramanujan graphs are related to communication network designs, and from a
theoretical point of view, link many branches of mathematics. In this thesis,
I investigated a class of graphs constructed from nilpotent matrices over finite fields. They are shown to be Ramanujan graphs. The spectrum of them, along
with some graph-theoretic properties were found.
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