Intrinsically Linked

Author

Eric W. Weisstein
July 1, 2009

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

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

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

Example

2-D

V5

ShowGraphArray[{CompleteGraph[6],CompleteGraph[3,3,1]}]

V7

GraphicsGrid[{Show[GraphData[#],PlotLabel->GraphData[#,"Notation"],BaseStyle->Italic]&/@{"K6","K1,3,3"}}]

3-D

Ed Pegg
Jan. 30, 2009

The simplest lattice without 4 coplanar points is the 3x3x2 grid.

pts=Flatten[Table[{a,b,c},{a,0,2},{b,0,2},{c,0,1}],2];

Eliminating symmetries, there are 20 different 6 point sets, no 4 on a plane.

Graphics3D[{Sphere[pts[[#]],.1]&/@{1,2,5,12,16,17},Tube[#,.05]&/@(pts[[#]]&/@Subsets[{1,2,5,12,16,17},{2}])},Boxed->False,SphericalRegion->True,ViewPoint->{3,-1,6}]