Minimally Curvy Graph

Author

Eric W. Weisstein
August 30, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/GraphTheory/MinimallyCurvyGraph.nb.

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

©2026 Wolfram Research, Inc. except for portions noted otherwise

Figure

TextGrid[minimallycurve=Sort[{GraphData[#,"NotationRules","MinimallyCurvy"],#}&/@GraphData["MinimallyCurvy"]],Dividers->All]

Minimal

GraphicsGrid[
	Outer[
		Function[{graphName, drawing},
			With[
				{
					label = Switch[
						drawing,
						"MinimalRectilinearCrossing", "rcn",
						"MinimalCrossing", "cn"
						],
					not = GraphData[graphName, "Notation"],
					index = If[
						Or[
							graphName === "SixteenCellGraph" && drawing === "MinimalCrossing",
							graphName === {"DoubleToroidal", {8, 8}} && drawing === "MinimalRectilinearCrossing"
						],
						2,
						1
						]
					},
				Annotate[
					StyleGraphs@
						GraphData[graphName, "Graph", drawing][[index]],
					PlotLabel -> Column[
						{
							If[
								MissingQ[not],
								Style[GraphData[graphName, "Name"], Italic],
								not /. s_String?LetterQ :> Style[s, Italic]
								],
							Row[
								{
									label,
									"==",
									GraphData[
										graphName,
										ToUpperCase[label]
										]
									},
								" "
								]
							},
						Alignment -> Center
						]
					]
				]
			],
		{
			"SixteenCellGraph",
			{"DoubleToroidal", {8, 8}}
			},
		{
			"MinimalRectilinearCrossing",
			"MinimalCrossing"
			},
		1
		],
	Alignment -> Bottom,
	Dividers -> All,
	BaseStyle -> {
		InsetBoxOptions -> {
			BaseStyle -> Directive[16, FontFamily -> "Times"]
			}
		}
	]

Embeddings

<<MathWorld`Graphs`

{"MinimallyCurvy", {8, 1}} == "SixteenCellGraph"

Names

GraphData[{"MinimallyCurvy",{8,1}},"StandardName"]

GraphData[{"MinimallyCurvy",{8,1}},"StandardNames"]

GraphData[{"MinimallyCurvy",{8,1}},{"V","CN","RCN"}]

{"MinimallyCurvy", {8, 2}} == {"DoubleToroidal", {8, 8}}

Names

GraphData[{"MinimallyCurvy",{8,2}},"StandardName"]

GraphData[{"MinimallyCurvy",{8,2}},"StandardNames"]

GraphData[{"MinimallyCurvy",{8,2}},{"V","CN","RCN"}]

GraphData

GraphDataClassString

GraphDataClassString["MinimallyCurvy"]

AddIndexedClass

AddIndexedClass["MinimallyCurvy",{"SixteenCellGraph"->{8,1},{"DoubleToroidal",{8,8}}->{8,2}},"15.1"]

RenameGraphFiles[]

GraphDataString

file=OpenWrite["~/minimally-curvy.m"]

WriteString[
file,
GraphDataString[
XXX,
"StandardName"->{"MinimallyCurvy",{9,1}},
"Name"->"9\[Hyphen]minimally curvy graph 1",
"NotationRules"->{"MinimallyCurvy"->{9,1}},
"Classes"->{"MinimallyCurvy"},
"Information"->"MinimallyCurvyGraph"
]
]

Close[file]