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Ramanujan graph
Known as:
Ramanujan graphs
In spectral graph theory, a Ramanujan graph, named after Srinivasa Ramanujan, is a regular graph whose spectral gap is almost as large as possible…
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Related topics
Related topics
8 relations
Adjacency matrix
Clique (graph theory)
Extremal graph theory
Girth (graph theory)
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Broader (1)
Algebraic graph theory
Papers overview
Semantic Scholar uses AI to extract papers important to this topic.
2020
2020
An Alon-Boppana theorem for powered graphs and generalized Ramanujan graphs
E. Abbe
,
Peter Ralli
arXiv.org
2020
Corpus ID: 219955978
The r-th power of a graph modifies a graph by connecting every vertex pair within distance r. This paper gives a generalization…
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2017
2017
Further results on discrete unitary invariance
Jesse T. Geneson
arXiv.org
2017
Corpus ID: 11441618
In arXiv:1607.06679, Marcus proved that certain functions of multiple matrices, when summed over the symmetries of the cube…
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2017
2017
Cubic Polynomials, Linear Shifts, and Ramanujan Cubics
Gregory P. Dresden
,
Prakriti Panthi
,
Anukriti Shrestha
,
Jiahao Zhang
2017
Corpus ID: 119640018
We show that every monic polynomial of degree three with complex coefficients and no repeated roots is either a (vertical and…
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2010
2010
Ramanujan graphs of very large girth based on octonions
X. Dahan
,
J. Tillich
2010
Corpus ID: 118276907
We present a generalization of the construction of graphs by Lubotzky, Phillips and Sarnak in their celebrated article "Ramanujan…
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2007
2007
On the Rigidity of Ramanujan Graphs
B. Servatius
2007
Corpus ID: 16293528
A graph G is generically [4] rigid in dimension one if and only if it contains a spanning tree, that is, a spanning subgraph…
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2007
2007
SECOND TALK ON RAMANUJAN GRAPHS
P. Clark
2007
Corpus ID: 1333947
We are especially interested in graphs – or better, in sequences of graphs – whose first eigenvalues λ1 are relatively small. In…
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2006
2006
Ramanujan Topologies for Decision Making in Sensor Networks
S. Kar
,
José M. F. Moura
2006
Corpus ID: 6150752
We consider the design of the topology of the communication graph G = (V, E) supporting distributed decision in sensor networks…
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2003
2003
RANDOM WALKS ON TREES AND RAMANUJAN GRAPHS
Tatiana Smirnova-Nagnibeda
2003
Corpus ID: 18063899
Different combinatorial techniques can be used successfully in the investigation of random walks on infinite graphs and more…
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2001
2001
Character sums, automorphic forms, equidistribution, and Ramanujan graphs 1
C. Chai
,
W. Li
2001
Corpus ID: 8001350
According to the Langlands program, L-functions arising from families of exponential sums over global function elds are…
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1997
1997
Optimal Cycle Codes Constructed From Ramanujan Graphs
J. Tillich
,
G. Zémor
SIAM Journal on Discrete Mathematics
1997
Corpus ID: 6159427
We aim here to show how some known Ramanujan Cayley graphs yield error-correcting codes that are asymptotically optimal in the…
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