GraphTheory
IsRamanujanGraph
test if graph is Ramanujan
Calling Sequence
Parameters
Options
Description
Definition
Ramanujan graphs in SpecialGraphs
Examples
Compatibility
IsRamanujanGraph(G,opts)
G
-
graph
opts
(optional) equation of the form parameters=true or parameters=false
parameters : keyword option of the form parameters=true or parameters=false. This specifies whether the parameters [d, lambda] should be returned when the graph is Ramanujan. The default is false.
The IsRamanujanGraph(G) command returns true if G is a Ramanujan graph and false otherwise.
An undirected graph G is Ramanujan if it is a regular graph with degree d and , where is the maximum of the absolute values of all the eigenvalues of the adjacency matrix of G excluding the greatest eigenvalue d.
These graphs are named after Srinivasa Ramanujan.
The following are graphs in the SpecialGraphs subpackage which are Ramanujan.
Graph
Number of Vertices
d
lambda
Petersen graph
10
3
Icosahedron graph
12
5
sqrt(5)
Clebsch graph
16
Complete graph
d-1
1
Paley graph
p
(q-1)/2
(sqrt(q)+1)/2
The GraphTheory[IsRamanujanGraph] command was introduced in Maple 2023.
For more information on Maple 2023 changes, see Updates in Maple 2023.
See Also
Degree
DegreeSequence
IsRegular
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