In spectral graph theory, a Ramanujan graph, named after Srinivasa Ramanujan, is a regular graph whose spectral gap is almost as large as possible… (More)

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2016

2016

- Michael B. Cohen
- 2016 IEEE 57th Annual Symposium on Foundations of…
- 2016

Recent work by Marcus, Spielman and Srivastava proves the existence of bipartite Ramanujan (multi) graphs of all degrees and all… (More)

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2016

2016

- Chris Hall, Doron Puder, William F. Sawin
- STOC
- 2016

Let <i>G</i> be a finite connected graph, and let ρ be the spectral radius of its universal cover. For example, if <i>G</i> is <i… (More)

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2015

Highly Cited

2015

- Charles Bordenave, Marc Lelarge, Laurent Massoulié
- 2015 IEEE 56th Annual Symposium on Foundations of…
- 2015

A non-backtracking walk on a graph is a directed path such that no edge is the inverse of its preceding edge. The non… (More)

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2013

Highly Cited

2013

- Adam Marcus, Daniel A. Spielman, Nikhil Srivastava
- 2013 IEEE 54th Annual Symposium on Foundations of…
- 2013

We prove that there exist infinite families of regular bipartite Ramanujan graphs of every degree bigger than 2. We do this by… (More)

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2009

2009

- Eyal Lubetzky
- 2009

A random n-lift of a base graph G is its cover graph H on the vertices [n]×V (G), where for each edge uv in G there is an… (More)

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2009

2009

- Eiichi Bannai, Osamu Shimabukuro, Hajime Tanaka
- Discrete Mathematics
- 2009

We consider finite analogues of Euclidean graphs in a more general setting than that considered in [A. Medrano, P. Myers, H.M… (More)

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2007

2007

- Reza Olfati-Saber
- 2007 American Control Conference
- 2007

In this paper, we explore spectral properties of a class of regular Cayley graphs known as Ramanujan graphs and prove that the… (More)

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2004

2004

- Eiichi Bannai, Osamu Shimabukuro, Hajime Tanaka
- Eur. J. Comb.
- 2004

This is a companion paper of “Finite Euclidean graphs and Ramanujan graphs” by the same authors. Finite analogues of the Poincar… (More)

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2003

2003

- Yair Glasner
- Combinatorica
- 2003

We construct an infinite family of (q + 1)−regular Ramanujan graphs Xn of girth 1. We also give covering maps Xn+1 → Xn such that… (More)

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1995

Highly Cited

1995

- Nabil Kahale
- J. ACM
- 1995

The spectral method is the best currently known technique to prove lower bounds on expansion. Ramanujan graphs, which have… (More)

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