Ustimenko Graph

Author

Eric W. Weisstein
March 17, 2021

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/UstimenkoGraph.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/UstimenkoGraph.html.

©2021 Wolfram Research, Inc. except for portions noted otherwise

Source

See [BCN1989] p. 279 or [VDKT2016] p. 22.

E. R. van Dam, J. H. Koolen, H. Tanaka, Distance Regular graphs, The Electronic Journal of Combinatorics. 2016

Andries E. Brouwer, Arjeh M. Cohen, and Arnold Neumaier. Distance-Regular Graphs, Springer, pp. 279-287, 1989.

On some properties of the geometries of the Chevalley groups and their generalizations

Construction

https://doc.sagemath.org/html/en/reference/graphs/sage/graphs/graph_generators.html#sage.graphs.graph_generators.GraphGenerators.UstimenkoGraph

┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.1, Release Date: 2020-05-20                     │
│ Using Python 3.7.3. Type "help()" for help.                        │
└────────────────────────────────────────────────────────────────────┘
sage: graphs.UstimenkoGraph(4,2)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-1-895d204975b3> in <module>()
----> 1 graphs.UstimenkoGraph(Integer(4),Integer(2))

/Applications/SageMath-9.1.app/Contents/Resources/sage/local/lib/python3.7/site-packages/sage/misc/lazy_import.pyx in sage.misc.lazy_import.LazyImport.__getattr__ (build/cythonized/sage/misc/lazy_import.c:3538)()
    319             True
    320         """
--> 321         return getattr(self.get_object(), attr)
    322 
    323     # We need to wrap all the slot methods, as they are not forwarded

AttributeError: 'GraphGenerators' object has no attribute 'UstimenkoGraph'

Select[Range[5],PrimePowerQ]

SageGraph[SageEvaluate["graphs.UstimenkoGraph(4,2)"]]

data=Table[{
{m,q},
TimeConstrained[SageGraph[SageEvaluate["graphs.UstimenkoGraph("<>ToString[m]<>","<>ToString[q]<>").edges()"]],10]
},{m,2,5},{q,{2,3,4,5}}]