Bipartite Dimension

Author

Eric W. Weisstein
June 26, 2026

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

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

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

GraphDataCountTable

table=GraphDataCountTable["BipartiteDimension"]

DateString[]

TextGrid[OEISUpdates[table],Dividers->All]

Parametrized families

<<MathWorld`Graphs`

Alkane

seq=Table[GraphData[{"Alkane",n},"BipartiteDimension"],{n,10}]

AlternatingGroupGraph

seq=Table[GraphData[{"AlternatingGroupGraph",n},"BipartiteDimension"],{n,2,6}]

Andrasfai

seq=Table[GraphData[{"Andrasfai",n},"BipartiteDimension"],{n,20}]

Antelope n×n

seq=Table[GraphData[{"Antelope",{n,n}},"BipartiteDimension"],{n,20}]

Antelope m×n

DeleteCases[
Flatten[Table[{
{m,n},
GraphData[{"Antelope",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}
]//Quiet

Antiprism

Entity["Graph",{"Antiprism",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Antiprism",n},"BipartiteDimension"],{n,3,25}]

Apollonian

seq=Table[GraphData[{"Apollonian",n},"BipartiteDimension"],{n,6}]

Barbell

seq=Table[GraphData[{"Barbell",n},"BipartiteDimension"],{n,3,20}]

Bishop n×n

seq=Table[GraphData[{"Bishop",{n,n}},"BipartiteDimension"],{n,20}]

Bishop m×n

Entity["Graph",{"Bishop",{m,n}}]["BipartiteDimension"]

DeleteCases[
Flatten[Table[{
{m,n},
GraphData[{"CompleteBipartite",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

BlackBishop n×n

seq=Table[GraphData[{"BlackBishop",{n,n}},"BipartiteDimension"],{n,20}]

BlackBishop m×n

Entity["Graph",{"Bishop",{m,n}}]["BipartiteDimension"]

DeleteCases[
Flatten[Table[{
{m,n},
GraphData[{"BlackBishop",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}
]//Quiet

Book

seq=Table[GraphData[{"Book",n},"BipartiteDimension"],{n,20}]

Bruhat

seq=Table[GraphData[{"Bruhat",n},"BipartiteDimension"],{n,6}]

Camel n×n

seq=Table[GraphData[{"Camel",{n,n}},"BipartiteDimension"],{n,20}]

Camel m×n

Entity["Graph",{"Camel",{m,n}}]["BipartiteDimension"]

DeleteCases[
Flatten[Table[{
{m,n},
GraphData[{"CompleteBipartite",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

Cameron

seq=Table[GraphData[{"Cameron",n},"BipartiteDimension"],{n,20}]

Centipede

seq=Table[GraphData[{"Centipede",n},"BipartiteDimension"],{n,10}]

CocktailParty

seq=Table[GraphData[{"CocktailParty",n},"BipartiteDimension"],{n,20}]

Complete

Entity["Graph",{"Complete",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Complete",n},"BipartiteDimension"],{n,30}]

CompleteBipartite n×n

Entity["Graph",{"CompleteBipartite",{n,n}}]["BipartiteDimension"]

seq=Table[GraphData[{"CompleteBipartite",{n,n}},"BipartiteDimension"],{n,20}]

CompleteBipartite m×n

Entity["Graph",{"CompleteBipartite",{m,n}}]["BipartiteDimension"]

DeleteCases[
Flatten[Table[{
{m,n},
GraphData[{"CompleteBipartite",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

CompleteTripartite n×n×n

Entity["Graph",{"CompleteTripartite",{n,n,n}}]["BipartiteDimension"]

seq=Table[GraphData[{"CompleteTripartite",{n,n,n}},"BipartiteDimension"],{n,10}]

CompleteTripartite k×m×n

Entity["Graph",{"CompleteTripartite",{k,m,n}}]["BipartiteDimension"]

DeleteCases[
Flatten[Table[{
{k,m,n},
GraphData[{"CompleteTripartite",{k,m,n}},"BipartiteDimension"],
XXX
},{n,10},{m,n},{k,m}],2],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

CompleteTripartiteMinusPerfectMatching

seq=Table[GraphData[{"CompleteTripartiteMinusPerfectMatching",{2n,2n,2n}},"BipartiteDimension"],{n,10}]

CossidentePenttila

{
#,
q=GraphData[#,"NotationRules","CossidentePenttila"],
XXX,
GraphData[#,"BipartiteDimension"]
}&/@GraphData["CossidentePenttila"]

CrossedPrism

seq=Table[GraphData[{"CrossedPrism",2n},"BipartiteDimension"],{n,2,12}]

Crown

seq=Table[GraphData[{"Crown",n},"BipartiteDimension"],{n,20}]

CubeConnectedCycle

Entity["Graph",{"CubeConnectedCycle",n}]["BipartiteDimension"]

seq=Table[GraphData[{"CubeConnectedCycle",n},"BipartiteDimension"],{n,3,8}]

Cycle

Entity["Graph",{"Cycle",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Cycle",n},"BipartiteDimension"],{n,3,30}]

CycleComplement

seq=Table[GraphData[{"CycleComplement",n},"BipartiteDimension"],{n,3,20}]

DiagonalIntersection

seq=Table[GraphData[{"DiagonalIntersection",n},"BipartiteDimension"],{n,3,14}]

Dipyramid

seq=Table[GraphData[{"Dipyramid",n},"BipartiteDimension"],{n,3,20}]

DorogovtsevGoltsevMendes

seq=Table[GraphData[{"DorogovtsevGoltsevMendes",n},"BipartiteDimension"],{n,0,7}]

DoubleCone

seq=Table[GraphData[{"DoubleCone",n},"BipartiteDimension"],{n,3,20}]

Empty

Entity["Graph",{"Empty",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Empty",n},"BipartiteDimension"],{n,30}]

ErectedPolygon

DeleteCases[Module[{n,r},
{
#,
{n,r}=GraphData[#,"NotationRules","ErectedPolygon"],
XXX,
GraphData[#,"BipartiteDimension"]
}
]&/@GraphData["ErectedPolygon"],
{__,x_,x_}]

FibonacciCube

seq=Table[GraphData[{"FibonacciCube",n},"BipartiteDimension"],{n,15}]

Fiveleaper n×n

seq=Table[GraphData[{"Fiveleaper",{n,n}},"BipartiteDimension"],{n,20}]

Fiveleaper m×n

Entity["Graph",{"Fiveleaper",{m,n}}]["BipartiteDimension"]

DeleteCases[
Flatten[Table[{
{m,n},
GraphData[{"Fiveleaper",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

Flower

seq=Table[GraphData[{"Flower",n},"BipartiteDimension"],{n,5,20}]

FoldedCube

seq=Table[GraphData[{"FoldedCube",n},"BipartiteDimension"],{n,2,10}]

Gear

seq=Table[GraphData[{"Gear",n},"BipartiteDimension"],{n,3,20}]

Giraffe n×n

seq=Table[GraphData[{"Giraffe",{n,n}},"BipartiteDimension"],{n,20}]

Giraffe m×n

Entity["Graph",{"Fiveleaper",{m,n}}]["BipartiteDimension"]

DeleteCases[
Flatten[Table[{
{m,n},
GraphData[{"Giraffe",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

Goldberg

seq=Table[GraphData[{"Goldberg",n},"BipartiteDimension"],{n,3,20}]

Grid n×n

Entity["Graph",{"Grid",{n,n}}]["BipartiteDimension"]

seq=Table[GraphData[{"Grid",{n,n}},"BipartiteDimension"],{n,20}]

Grid m×n

Entity["Graph",{"Grid",{m,n}}]["BipartiteDimension"]

Sort@DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"Grid",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

Grid n×n×n

Entity["Graph",{"Grid",{n,n,n}}]["BipartiteDimension"]

seq=Table[GraphData[{"Grid",{n,n,n}},"BipartiteDimension"],{n,10}]

Grid k×m×n

Entity["Graph",{"Grid",{k,m,n}}]["BipartiteDimension"]

Sort@DeleteCases[Flatten[Table[{
{k,m,n},
GraphData[{"Grid",{k,m,n}},"BipartiteDimension"],
XXX
},{n,10},{m,n},{k,m}],2],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

HalvedCube

seq=Table[GraphData[{"HalvedCube",n},"BipartiteDimension"],{n,10}]

Hanoi

seq=Table[GraphData[{"Hanoi",n},"BipartiteDimension"],{n,6}]

Helm

seq=Table[GraphData[{"Helm",n},"BipartiteDimension"],{n,3,20}]

Hypercube

Entity["Graph",{"Hypercube",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Hypercube",n},"BipartiteDimension"],{n,0,10}]

KC

DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"KC",{m,n}},"BipartiteDimension"],
XXX
},{n,3,10},{m,10}],1],{_,x_,x_}]

Keller

Entity["Graph",{"Keller",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Keller",n},"BipartiteDimension"],{n,5}]

King n×n

seq=Table[GraphData[{"King",{n,n}},"BipartiteDimension"],{n,20}]

King m×n

Sort@DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"King",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

Knight n×n

Entity["Graph",{"Knight",{n,n}}]["BipartiteDimension"]

seq=Table[GraphData[{"Knight",{n,n}},"BipartiteDimension"],{n,20}]

Knight m×n

Entity["Graph",{"Knight",{m,n}}]["BipartiteDimension"]

Sort@DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"King",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

KP

DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"KP",{m,n}},"BipartiteDimension"],
XXX
},{n,10},{m,10}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

Ladder

Entity["Graph",{"Ladder",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Ladder",n},"BipartiteDimension"],{n,20}]

LadderRung

seq=Table[GraphData[{"LadderRung",n},"BipartiteDimension"],{n,20}]

LindgrenSousselier

seq=Table[GraphData[{"LindgrenSousselier",n},"BipartiteDimension"],{n,11}]

LucasCube

seq=Table[GraphData[{"LucasCube",n},"BipartiteDimension"],{n,15}]

MengerSponge

seq=Table[GraphData[{"MengerSponge",n},"BipartiteDimension"],{n,3}]

MoebiusLadder

Entity["Graph",{"MoebiusLadder",n}]["BipartiteDimension"]

seq=Table[GraphData[{"MoebiusLadder",n},"BipartiteDimension"],{n,3,25}]

Mycielski

Entity["Graph",{"Mycielski",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Mycielski",n},"BipartiteDimension"],{n,11}]

Necklace

seq=Table[GraphData[{"Necklace",n},"BipartiteDimension"],{n,10}]

Odd

Entity["Graph",{"Odd",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Odd",n},"BipartiteDimension"],{n,7}]

Paley

{
#,
q=GraphData[#,"NotationRules","Paley"],
XXX,
GraphData[#,"BipartiteDimension"]
}&/@GraphData["Paley"]

Pan

seq=Table[GraphData[{"Pan",n},"BipartiteDimension"],{n,3,20}]

Path

Entity["Graph",{"Path",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Path",n},"BipartiteDimension"],{n,20}]

PathComplement

seq=Table[GraphData[{"PathComplement",n},"BipartiteDimension"],{n,20}]

Peisert

{
#,
q=GraphData[#,"NotationRules","Peisert"],
XXX,
GraphData[#,"BipartiteDimension"]
}&/@GraphData["Peisert"]

Pell

seq=Table[GraphData[{"Pell",n},"BipartiteDimension"],{n,9}]

PlummerToft

seq=Table[GraphData[{"PlummerToft",n},"BipartiteDimension"],{n,20}]

Prism

Entity["Graph",{"Prism",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Prism",n},"BipartiteDimension"],{n,3,25}]

Queen n×n

seq=Table[GraphData[{"Queen",{n,n}},"BipartiteDimension"],{n,20}]

Queen m×n

Sort@DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"Queen",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

Rook n×n

seq=Table[GraphData[{"Rook",{n,n}},"BipartiteDimension"],{n,20}]

Rook m×n

Sort@DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"Rook",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

RookComplement n×n

seq=Table[GraphData[{"RookComplement",{n,n}},"BipartiteDimension"],{n,20}]

RookComplement m×n

Sort@DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"RookComplement",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

SierpinskiCarpet

seq=Table[GraphData[{"SierpinskiCarpet",n},"BipartiteDimension"],{n,4}]

SierpinskiGasket

seq=Table[GraphData[{"SierpinskiGasket",n},"BipartiteDimension"],{n,7}]

SierpinskiTetrahedron

seq=Table[GraphData[{"SierpinskiTetrahedron",n},"BipartiteDimension"],{n,6}]

Spoke n×n

seq=Table[GraphData[{"Spoke",{n,n}},"BipartiteDimension"],{n,5}]

StackedBook n×n

seq=Table[GraphData[{"StackedBook",{n,n}},"BipartiteDimension"],{n,10}]

StackedBook m×n

DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"StackedBook",{m,n}},"BipartiteDimension"],
XXX
},{n,10},{m,n}],1],{_,x_,x_}]

StackedPrism n×n

seq=Table[GraphData[{"StackedPrism",{n,n}},"BipartiteDimension"],{n,3,5}]

StackedPrism m×n

DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"StackedPrism",{m,n}},"BipartiteDimension"],
XXX
},{m,3,8},{n,5}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

Star

Entity["Graph",{"Star",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Star",n},"BipartiteDimension"],{n,25}]

Sun

seq=Table[GraphData[{"Sun",n},"BipartiteDimension"],{n,3,20}]

Sunlet

seq=Table[GraphData[{"Sunlet",n},"BipartiteDimension"],{n,3,20}]

Tetrahedral

seq=Table[GraphData[{"Tetrahedral",n},"BipartiteDimension"],{n,6,10}]

TorusGrid n×n

seq=Table[GraphData[{"TorusGrid",{n,n}},"BipartiteDimension"],{n,3,20}]

TorusGrid m×n

Sort@DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"TorusGrid",{m,n}},"BipartiteDimension"],
XXX
},{n,3,20},{m,3,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

Transposition

Entity["Graph",{"Transposition",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Transposition",n},"BipartiteDimension"],{n,6}]

Trapezohedron

Entity["Graph",{"Trapezohedron",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Trapezohedron",n},"BipartiteDimension"],{n,3,20}]

Triangular

seq=Table[GraphData[{"Triangular",n},"BipartiteDimension"],{n,2,20}]

TriangularGrid

seq=Table[GraphData[{"TriangularGrid",n},"BipartiteDimension"],{n,0,20}]

TriangularHoneycombAcuteKnight

seq=Table[GraphData[{"TriangularHoneycombAcuteKnight",n},"BipartiteDimension"],{n,20}]

TriangularHoneycombBishop

seq=Table[GraphData[{"TriangularHoneycombBishop",n},"BipartiteDimension"],{n,20}]

TriangularHoneycombObtuseKnight

seq=Table[GraphData[{"TriangularHoneycombObtuseKnight",n},"BipartiteDimension"],{n,20}]

TriangularHoneycombQueen

seq=Table[GraphData[{"TriangularHoneycombQueen",n},"BipartiteDimension"],{n,20}]

TriangularHoneycombRook

seq=Table[GraphData[{"TriangularHoneycombRook",n},"BipartiteDimension"],{n,20}]

TriangularSnake

seq=Table[GraphData[{"TriangularSnake",n},"BipartiteDimension"],{n,1,20,2}]

TruncatedSquareLattice n×n

seq=Table[GraphData[{"TruncatedSquareLattice",{n,n}},"BipartiteDimension"],{n,10}]

TruncatedSquareLattice m×n

Sort@DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"TruncatedSquareLattice",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

Web

seq=Table[GraphData[{"Web",n},"BipartiteDimension"],{n,3,20}]

Wheel

Entity["Graph",{"Wheel",n}]["BipartiteDimension"]

seq=Table[GraphData[{"Wheel",n},"BipartiteDimension"],{n,4,20}]

WheelComplement

seq=Table[GraphData[{"WheelComplement",n},"BipartiteDimension"],{n,4,20}]

WhiteBishop n×n

seq=Table[GraphData[{"WhiteBishop",{n,n}},"BipartiteDimension"],{n,2,20}]

WhiteBishop m×n

Sort@DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"WhiteBishop",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet

WhiteCamel n×n

seq=Table[GraphData[{"Bishop",{n,n}},"BipartiteDimension"],{n,{5}}]

Zebra n×n

seq=Table[GraphData[{"Zebra",{n,n}},"BipartiteDimension"],{n,20}]

Zebra m×n

Sort@DeleteCases[Flatten[Table[{
{m,n},
GraphData[{"Zebra",{m,n}},"BipartiteDimension"],
XXX
},{n,20},{m,n}],1],
{_,x_,x_}|{_,_GraphData,_}]//Quiet