Ramanujanovi grafi : magistrsko delo

Petrič, Tadej (author), Jezernik, Urban (mentor)

V delu si ogledamo definicijo Ramanujanovih grafov, kako jih generiramo z naključnimi metodami, dva načina eksplicitne konstrukcije Ramanujanovih grafov ter dokažemo analog Riemannove hipoteze za teorijo grafov.

• Language: Slovenian
• Keywords: Ramanujanovi grafi, prepletene družine, Ramanujanova domneva, Ihara zeta funkcija
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2025
• PID: 20.500.12556/RUL-170850
• UDC: 519.1
• COBISS.SI-ID: 242581251
• Publication date in RUL: 18.07.2025

Secondary language

• Language: English
• Title: Ramanujan graphs

Abstract

In this thesis, we define Ramanujan graphs. Then we explore different methods to generate them, including stochastic methods and two explicit constructions. Finally, we prove the analogue of the Riemann hypothesis for graph theory.

• Keywords: Ramanujan graphs, interlacing families, Ramanujan conjecture, Ihara zeta function