NDLI: Ramanujan Diagrams

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Volume 32

Volume 31

Homomorphic Zero-Knowledge Threshold Schemes over any Finite Abelian Group

New $\frac{3}{4}$-Approximation Algorithms for the Maximum Satisfiability Problem

Treewidth of Circular-Arc Graphs

Optimal Parallel Algorithms for Straight-Line Grid Embeddings of Planar Graphs

A Linear-Time Algorithm for Isomorphism of Graphs of Bounded Average Genus

Further Results on T-Coloring and Frequency Assignment Problems

On Universal Cycles for k-Subsets of an n-Set

Drawing Graphs on Surfaces

A New Class of Pyramidally Solvable Symmetric Traveling Salesman Problems

On Path-Tough Graphs

Ramanujan Diagrams

Generalized Hamming Weights of Melas Codes and Dual Melas Codes

A Coding Approach to Signed Graphs

Predicting Cause-Effect Relationships from Incomplete Discrete Observations

Ramanujan Diagrams

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Morgenstern, Moshe
Copyright Year	1994
Abstract	A diagram D is a graph that is of finite volume with respect to a measure (weights) on the vertices and edges. The author gives the basic definitions for a diagram, and defines the cases where it is an expander. Let $\Delta $ be the Laplacian on $L_2 ( D )$, and let $\lambda $ be the infimum of its spectrum on the subspace of functions that are orthogonal to the constant function. The strong connection between $\lambda $ being large and D being a good expander is shown. For a k-regular infinite diagram, the largest possible $\lambda $ is $k - 2\sqrt {k - 1} $, and when this is achieved, it is called a Ramanujan diagram. Using representation theory of $PGL_2 $, many infinite families of infinite Ramanujan diagrams are explicitly constructed.
Starting Page	560
Ending Page	570
Page Count	11
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480192235325
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	7
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	1994-11-01
Access Restriction	Subscribed
Subject Keyword	diagram Graphs and abstract algebra explicit constructions Extremal problems Ramanujan graph/diagram expander Laplacian
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Extremal Cayley Digraphs of Finite Cyclic Groups

New and explicit constructions of unbalanced Ramanujan bipartite graphs

Ramanujan coverings of graphs

Families of ramanujan graphs and quaternion algebras.

Examples of Ramanujan and expander graphs for practical applications

Graphs from Generalized Kac--Moody Algebras

Twice-ramanujan sparsifiers

Monotone expansion

Lower Bounds for the Isoperimetric Numbers of Random Regular Graphs

Ramanujan Diagrams

Similar Documents

Extremal Cayley Digraphs of Finite Cyclic Groups

New and explicit constructions of unbalanced Ramanujan bipartite graphs

Ramanujan coverings of graphs

Families of ramanujan graphs and quaternion algebras.

Examples of Ramanujan and expander graphs for practical applications

Graphs from Generalized Kac--Moody Algebras

Twice-ramanujan sparsifiers

Monotone expansion

Lower Bounds for the Isoperimetric Numbers of Random Regular Graphs

Ramanujan Diagrams