• Corpus ID: 238259150

On Near Optimal Spectral Expander Graphs of Fixed Size

  title={On Near Optimal Spectral Expander Graphs of Fixed Size},
  author={Clark Alexander},
We present two powerful heuristic methods for building random regular graphs and finding a near optimal spectral gap in a finite regular graph. 


Explicit constructions of linear size superconcentrators
  • O. Gabber, Z. Galil
  • Mathematics
    20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
  • 1979
We present an explicit construction of an infinite family of N-superconcentrators of density 44. The most economical previously known explicit graphs of this type have density around 60.
A Note on Consistent Rotation Maps of Graph Cartesian Products
Given two regular graphs with consistent rotation maps, a constructive method for a consistent rotation map on their Cartesian product is produced as a simple set of rules of addition and table look ups.
Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees
The existence of infinite families of (c, d)-biregular bipartite graphs with all non-trivial eigenvalues bounded by √c-1+√d-1, for all c, d ≥ q 3 is proved.
Relative expanders or weakly relatively Ramanujan graphs
Let G be a fixed graph with largest (adjacency matrix) eigenvalue λ0 and with its universal cover having spectral radius ρ. We show that a random cover of large degree over G has its “new”
Models of random regular graphs
This is a survey of results on properties of random regular graphs, together with an exposition of some of the main methods of obtaining these results. Related results on asymptotic enumeration are
The Limiting Eigenvalue Distribution of Iterated k-Regular Graph Cylinders
The original question was whether or not the graph cylinder construction would produce an expander graph that is a suitable candidate for the neural networks being developed at Nousot, and this question is answered in the negative for computational purposes.
Existence and Explicit Constructions of q + 1 Regular Ramanujan Graphs for Every Prime Power q
For any prime power q, explicit constructions for many infinite linear families of q + 1 regular Ramanujan graphs are given as Cayley graphs of PGL2 or PSL2 over finite fields, with respect to very simple generators.
Fullerene Graphs and Some Relevant Graph Invariants
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and
Ramanujan graphs and Hecke operators
We associate to the Hecke operator Tp , p a prime, acting on a space of theta series an explicit p + 1 regular Ramanujan graph G having large girth. Such graphs have high "magnification" and thus