Obtain a list of all standard implemented graphs:
Obtain a list of all implemented graphs:
Find the English name of a graph:
A list of alternate names can also be found:
Additional names acceptable as input can be found:
Find the list of graph classes:
Find the list of named graphs belonging to a class:
Test whether a graph belongs to a class:
Get a list of properties for a particular graph:
Get a short textual description of a property:
Get a longer textual description:
A property value can be any valid
Mathematica expression:
A property that is not available for a graph has the value
Missing["NotAvailable"]:
Some graph properties may be
Missing but still include partial information:
A property whose value is too large to include has the value
Missing["TooLarge"]:
Give the adjacency matrix, returned as a
SparseArray object:
Convert to an explicit matrix:
Plot the matrix using
ArrayPlot:
Return distance matrix of the octahedral graph:
Return the number of edges of the octahedral graph:
List the indices of edges of the octahedral graph:
Return the edges as a set of rules, suitable for plotting in
GraphPlot:
Show the faces of the octahedral graph:
Give the incidence matrix the octahedral graph:
Give it in expanded form:
Give the Laplacian matrix the octahedral graph:
Give it in expanded form:
Give the normalized Laplacian matrix the octahedral graph:
Give it in expanded form:
Show the faces of the octahedral graph:
List all connected graphs:
List connected graphs on five vertices:
Check if the graph
is connected:
Check if the graph
is connected:
List the indices of the connected components of the
graph:
List the number of connected components:
List the names of the connected components:
List disconnected graphs on five vertices:
Check if the graph
is disconnected:
Check if the graph
is disconnected:
Find the edge connectivity of a complete binary tree of order 4:
Give the vertex connectivity of Tietze's graph:
Show all available images of the octahedral graph:
Return the vertex coordinates for all embeddings:
Show the default embedding of the octahedral graph:
Show the three-dimensional embedding of the octahedral graph returned by
GraphPlot3D:
Show a labeled version of the default embedding of the octahedral graph:
Return the vertex coordinates for the default embedding:
Display the characteristic polynomial of the Coxeter graph as a pure function:
As a function of a variable
x:
Compare with the directly computed value:
Give the chromatic polynomial of the cubical graph as a pure function:
As a function of a variable
x:
The chromatic polynomial is a special case of the rank polynomial:
Give the chromatic polynomial of the icosahedral graph in terms of a variable
x:
Give the flow polynomial of the cubical graph as a function of a variable
u:
The flow polynomial is a special case of the rank polynomial:
Give the idiosyncratic polynomial of the cubical graph:
Compare with a direct computation:
Give the independence polynomial of the cubical graph:
Give the matching polynomial of the cubical graph:
Give the rank polynomial of the cubical graph:
Give the reliability polynomial of the cubical graph:
The reliability polynomial is a special case of the Tutte polynomial:
Give the sigma polynomial of the cubical graph:
Give the Tutte polynomial of the cubical graph:
The Tutte polynomial is a special case of the rank polynomial:
Chromatically unique graphs:
The cubical graph is chromatically unique:
The antenna graph is not:
Display the Balaban index of the Coxeter graph:
Give the Balaban index of the isobutane graph:
Give the cyclomatic number (
i.e., circuit rank) of the Coxeter graph:
Display the cyclomatic number of the icosahedral graph:
Compare with the value obtained from other properties:
Give the Hosoya index of the cubical graph:
Give the Kirchhoff index of the cubical graph:
Give the Kirchhoff index of the isobutane graph:
Give the Kirchhoff sum index of the cubical graph:
Give the Kirchhoff sum index of the isobutane graph:
Give the stability index of the cubical graph:
Give the Wiener index of the cubical graph:
Give the Wiener index of the isobutane graph:
Give the Wiener sum index of the cubical graph:
Give the Wiener sum index of the isobutane graph:
Display the arc transitivity of the Coxeter graph:
Find graphs having articulation vertices:
Give the order of the automorphism group of the octahedral graph:
Explicitly give the automorphisms of the octahedral graph:
Find graphs having bridges:
List the chromatically unique graphs on 6 or fewer vertices:
Check if the square graph is chromatically unique:
Show the chromatic number of the icosahedral graph:
Display the clique number of the icosahedral graph:
Display the corank of the icosahedral graph:
Compute the corank from other graph properties:
Display the crossing number of the icosahedral graph:
The crossing number is 0 since the graph is planar:
Show the vertex degrees of the claw graph:
Give the graphs on four or fewer vertices that are determined by resistance:
Check if the cubical graph is determined by spectrum:
Check if the tesseract graph is determined by spectrum:
Give the names of the graphs with the same spectrum as the tesseract graph:
Give the diameter of the Pappus graph:
Give the eccentricities of the Pappus graph:
Return the edge chromatic number of the 120-cell graph:
Give the genus of the cubical graph:
Display the girth of the Petersen graph:
Return the number of Hamiltonian cycles of the cubical graph:
List the Hamiltonian cycles of the cubical graph:
Return the number of Hamiltonian paths of the tetrahedral graph:
Return the Hamiltonian paths of the cubical graph:
Return the independence number of the Heawood graph:
Return the Lovász number of the 5-cycle graph:
Display the rank of the icosahedral graph:
Compute the corank from other graph properties:
Give the rectilinear crossing numbers for complete graphs:
Give the resistance matrix of the cubical graph:
Display the Shannon capacity of the cubical graph:
Display the number of spanning trees in the 120-cell graph:
Display the spectrum of the 600-cell graph:
Display a nicely formatted version:
Give the toroidal crossing numbers for complete graphs:
List the unitransitive graphs:
Produce a table of the unitransitivity of the above graphs:
List the alternate English names of the tesseract graph:
Show the alternate standard names for the tesseract graph:
Show graph names for graphs that are cochromatic with the claw graph:
Show graph names for graphs that are cochromatic with the 5-star graph:
Give the names of graphs cochromatic with the bull graph:
Give the name of the graph complement of the cubical graph:
Show the graph names for the complement of graphs on four or fewer vertices:
The complement graph name of a self-complementary graph is identical to the
StandardName:
Show graphs that share a resistance multiset with at least one other distinct graph:
List the names of graphs sharing the same multiset of resistances with a given graph:
Show graph names for graphs that are equivalent with a particular 20-vertex graph:
Give the names of graphs cospectral with the Shrikhande graph:
Show graph names for graphs that are cospectral with the tesseract graph:
Show the graph name for the graph that is dual to the tesseract graph:
It is in turn dual to the tesseract graph:
List graphs with a tabulated graph dual:
Show the name of the graph dual of the 24-cell graph:
Show that the 24-cell graph and tesseract graph are dual to one another:
Display the quartic transitive graph Qt66:
Verify that it is dual to itself:
Self-dual graphs are dual to themselves:
Give the name of the line graph for the Petersen graph:
Give the names of the line graphs of the Platonic graphs:
Show the Platonic graphs and their line graphs:
Show the graph names for the line graphs of graphs on four or fewer vertices:
Taking the line graph twice does not in general give back the original graph:
The line graph of a graph is isomorphic to itself only for cycle graphs or unions of identical cycle graphs:
Give the textual name of the octahedral graph:
Give the name of the complete graph
:
Verify the standard name for this graph:
Give a list of rules for notations associated with the complete graph
:
Give rules for various notations for the octahedral graph:
Query the standard name of the 4-hypercube graph:
Show other alternate standard names corresponding to this standard name:
Give the standard name of the complete graph
:
Hamilton-connected graphs:
Graphs that provide counterexamples to Kempe's purported proof of the four-color theorem:
Distance-transitive graphs:
Vertex-transitive graphs:
LCF (regular Hamiltonian) graphs:
Self-complementary graphs:
(Generalized) prism graphs:
Regular polychoron graphs:
Complete bipartite graphs:
Complete tripartite graphs:
Generalized polygon graphs:
simple graph with n vertices.
with horizontal edges removed
(n)
with a vertex in common
EXAMPLES
Basic Examples 
Scope 