Graph Subdivision

Author

Eric W. Weisstein
June 9, 2023

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

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

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

Figure

vs=Subscript[v,#]&/@{i,j,k};
font=Directive[14,FontFamily->"Times"];
style=Sequence[VertexSize->{"Scaled",.1},VertexStyle->Red,EdgeStyle->Black,VertexLabels->Automatic,VertexLabelStyle->font,EdgeLabelStyle->font];

Magnify[Row[{
Graph[
vs[[{1,-1}]],
{Labeled[UndirectedEdge@@vs[[{1,-1}]],e,{.5,{0,1.3}}]},
VertexCoordinates->{{0,0},{1,0}},style],
"⟶",
Graph[
vs,
Labeled[UndirectedEdge@@#,#2,{.5,{.2,1.3}}]&@@@Transpose[{Partition[vs,2,1],Superscript[e,#]&/@{′,′′}}],
VertexCoordinates->{{0,0},{1/2,0},{1,0}},
style]
},Spacer[2]],2]