Suzuki Tower

Author

Eric W. Weisstein
June 10, 2009

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

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

©2009 Wolfram Research, Inc. except for portions noted otherwise

Tower

g=NestList[LocalGraph,Graph["SuzukiGraph"],4]

l=RecognizeGraph/@%

Grid[GraphData[#,{"V","Name"}]&/@l,Dividers->All,Alignment->{{Decimal,Left},Automatic}]//TraditionalForm

Grid[{V[#],FastAutomorphismCount[#]}&/@g,Dividers->All,Alignment->{Right,Automatic}]//TraditionalForm

Hamiltonian Paths

FastHamiltonianQ[g3]//Timing

Length[h=HamiltonianCycles[g3,All]]//Timing

GraphData

GraphDataString

file=OpenWrite["suztow.m"]

WriteString[file,GraphDataString[g1,
"Name"->"G_2(4) graph",
"StandardName"->"G24Graph",
"Vertices"->None,
"Source"->"Suzuki Tower",
"Skip"->{"ClawFree"},
"Notation"->Row[{Subscript["G",2],"(",4,")"}],
Debug->True,
TimeConstraint->60
]]//Timing

WriteString[file,GraphDataString[g3,
"Name"->"U_3(3) graph",
"StandardName"->"U33Graph",
"Vertices"->None,
"Source"->"Suzuki Tower",
"Notation"->Row[{Subscript["U",3],"(",3,")"}],
Debug->True,
TimeConstraint->60
]]//Timing

Close[file]