Longhorn Graph

Author

Eric W. Weisstein
May 13, 2008

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

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Images

GraphicsGrid[Partition[GraphData["LonghornGraph","AllImages"],3,3,{1,1},{}],Spacings->{0,-70}]

GraphData["LonghornGraph","Images","UnitDistance"]

ShowLabeledGraph[g=GraphData["LonghornGraph","Graphs"][[1]]]

GetGraphData["LonghornGraph","File"]

ShowLabeledGraph[g1=Graph[List/@{{1,2},{2,3},{3,5},{3,4},{4,5},{5,6},{6,7}},List/@{{0,0},{1,0},{2,0},{5/2,-(Sqrt[3])/2},{3,0},{4,0},{5,0}}]]

Norm/@Subtract@@@(Vertices[g][[#]]&/@Edges[g])

ShowLabeledGraph[g2=Graph[List/@{{1,2},{2,3},{3,5},{3,4},{4,5},{5,6},{6,7}},List/@{{1,1},{1,0},{2,0},{5/2,-(Sqrt[3])/2},{3,0},{4,0},{4,1}}]]

ShowLabeledGraph[g3=Graph[List/@{{1,2},{2,3},{3,5},{3,4},{4,5},{5,6},{6,7}},List/@{{1,0},{3/2,-(Sqrt[3])/2},{2,0},{5/2,-(Sqrt[3])/2},{3,0},{7/2,-(Sqrt[3])/2},{4,0}}]]

Norm/@Subtract@@@(Vertices[g][[#]]&/@Edges[g])

ShowLabeledGraph[g4=Graph[List/@{{1,2},{2,3},{3,5},{3,4},{4,5},{5,6},{6,7}},List/@{{1,-(Sqrt[3])},{3/2,-(Sqrt[3])/2},{2,0},{5/2,-(Sqrt[3])/2},{3,0},{7/2,-(Sqrt[3])/2},{4,-(Sqrt[3])}}]]

Norm/@Subtract@@@(Vertices[g][[#]]&/@Edges[g])

ShowLabeledGraph[g5=Graph[List/@{{1,2},{2,3},{3,5},{3,4},{4,5},{5,6},{6,7}},List/@{{2,-(Sqrt[3])},{3/2,-(Sqrt[3])/2},{2,0},{5/2,-(Sqrt[3])/2},{3,0},{7/2,-(Sqrt[3])/2},{3,-(Sqrt[3])}}]]

Norm/@Subtract@@@(Vertices[g][[#]]&/@Edges[g])

ToCommonEdges[#,"LonghornGraph"]&/@{g1,g2,g3,g4,g5}

GraphData

Subjects

GraphClassString["LonghornGraph"]

Matrices

GraphDataMatrices["LonghornGraph"]

Construction

ShowLabeledGraph[g=Graph[List/@{{1,2},{2,3},{3,4},{4,5},{5,6},{3,7},{4,7}},List/@{{-3/2,0},{-1,0},{-1/2,0},{1/2,0},{1,0},{3/2,0},{0,-Sqrt[2]/2}}]]

rg=RecognizeGraph[g]

ToCommonEdges[g,Graph[{7,381}]]