منابع مشابه
Hypergraph expanders from Cayley graphs
We present a simple mechanism, which can be randomised, for constructing sparse 3-uniform hypergraphs with strong expansion properties. These hypergraphs are constructed using Cayley graphs over Z2 and have vertex degree which is polylogarithmic in the number of vertices. Their expansion properties, which are derived from the underlying Cayley graphs, include analogues of vertex and edge expans...
متن کاملRandom Cayley Graphs and Expanders
For every 1 > δ > 0 there exists a c = c(δ) > 0 such that for every group G of order n, and for a set S of c(δ) log n random elements in the group, the expected value of the second largest eigenvalue of the normalized adjacency matrix of the Cayley graph X(G,S) is at most (1−δ). This implies that almost every such a graph is an ε(δ)-expander. For Abelian groups this is essentially tight, and ex...
متن کاملCayley graphs containing expanders, after Gromov
We give the sketch of a combinatorial proof of the construction by Gromov of a group whose Cayley graph contains a family of expanders. Combining the methods in [Oll1] and [Oll2], it is possible to give a proof of the construction invented by M. Gromov in [G] that there is an infinite group whose Cayley graph contains (in some quasi-isometric sense) a family of expanders. We only give the main ...
متن کاملQuantum expanders from any classical Cayley graph expander
We give a simple recipe for translating walks on Cayley graphs of a group G into a quantum operation on any irrep of G. Most properties of the classical walk carry over to the quantum operation: degree becomes the number of Kraus operators, the spectral gap becomes the gap of the quantum operation (viewed as a linear map on density matrices), and the quantum operation is efficient whenever the ...
متن کاملCayley graphs - Cayley nets
It is, however, not clear how to choose the generators to produce special graphs. We know many topologies and their generators, but many more may be constructed in the future, having better properties (in terms of diameter, nodal degree and connectivity) than for instance the hypercube. I will present several graphs which connect rings using the generator g 1 and some additional generators.
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2019
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-019-1895-1