scholarly journals Spectra of lifted Ramanujan graphs

2011 ◽  
Vol 227 (4) ◽  
pp. 1612-1645 ◽  
Author(s):  
Eyal Lubetzky ◽  
Benny Sudakov ◽  
Van Vu
Keyword(s):  
Ramanujan Graphs

scholarly journals On an anti-Ramsey property of Ramanujan graphs

1995 ◽  
Vol 6 (4) ◽  
pp. 417-431 ◽  
Author(s):  
P. E. Haxell ◽  
Y. Kohayakawa
Keyword(s):  
Ramsey Property ◽  
Ramanujan Graphs

scholarly journals Gap sets for the spectra of cubic graphs

2021 ◽  
Vol 1 (1) ◽  
pp. 1-38
Author(s):  
Alicia Kollár ◽  
Peter Sarnak
Keyword(s):  
Line Graphs ◽  
Cubic Graphs ◽  
Content Type ◽  
Ramanujan Graphs ◽  
Adjacency Matrices

We study gaps in the spectra of the adjacency matrices of large finite cubic graphs. It is known that the gap intervals ( 2 2 , 3 ) (2 \sqrt {2},3) and [ − 3 , − 2 ) [-3,-2) achieved in cubic Ramanujan graphs and line graphs are maximal. We give constraints on spectra in [ − 3 , 3 ] [-3,3] which are maximally gapped and construct examples which achieve these bounds. These graphs yield new instances of maximally gapped intervals. We also show that every point in [ − 3 , 3 ) [-3,3) can be gapped by planar cubic graphs. Our results show that the study of spectra of cubic, and even planar cubic, graphs is subtle and very rich.

scholarly journals Ramanujan graphs and exponential sums over function fields

2020 ◽  
Vol 217 ◽  
pp. 44-77
Author(s):  
Naser T. Sardari ◽  
Masoud Zargar
Keyword(s):  
Exponential Sums ◽  
Function Fields ◽  
Ramanujan Graphs
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