Knödel Graph

Author

Eric W. Weisstein
March 30, 2020

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

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

©2020 Wolfram Research, Inc. except for portions noted otherwise

Definition

KnoedelGraph[3,10]

KnoedelGraph[3,10,VertexLabels->"Name"]

Special cases

special=Sort@Flatten[Table[{{d,n},RecognizeGraph[KnoedelGraph[d,n]]},{n,2,50,2},{d,Floor[Log2[n]]}],1]

DeleteCases[Cases[special,{p_,{}}:>p],{1|2,_}]

knoedel=Rule@@@(Reverse/@DeleteCases[special,{_,{}}])

(1, 2n) are ladder rung graphs 2n (Subscript[P, 2])
(2, 2n) are cycle graphs (Subscript[C, 2n])
(3, 2n) are honeycomb toroidal graphs (1, 2n, 5)

TextGrid[knoedel=DeleteCases[special,{_,{}|{"Cycle"|"LadderRung",_}}],Dividers->All]