Delsarte Bound

Author

Eric W. Weisstein
November 20, 2023

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

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

©2023 Wolfram Research, Inc. except for portions noted otherwise

Source

https://arxiv.org/pdf/2311.09001.pdf

Satisfy the Delsarte bound:

Length[defined=Select[GraphData[{"Connected","DistanceRegular"},2;;],ListQ@GraphData[#,"Cliques"]&]]

DeleteCases[Monitor[{g=#,AllTrue[GraphData[#,"Cliques"],Function[c,Length[c]≤1+((GraphData[#,"MinimumVertexDegree"])/(Abs[GraphData[#,"Spectrum"][[1]]]))]]}&/@defined,g],
{_,True}]//Timing

Contains a Delsarte clique:

Cases[Monitor[{g=#,AnyTrue[GraphData[#,"Cliques"],Function[c,Length[c]==1+((GraphData[#,"MinimumVertexDegree"])/(Abs[GraphData[#,"Spectrum"][[1]]]))]]}&/@defined,g],
{gn_,True}:>gn]//Timing