Graph name

Graph caption
Named afterPerson's name
VerticesVertices
EdgesEdges
RadiusRadius
DiameterDiameter
GirthGirth
Chromatic numberChromatic number
Chromatic indexChromatic index
PropertiesMiscellaneous properties

Petersen graph
Named afterJulius Petersen
Vertices10
Edges15
Radius2
Diameter2
Girth5
Chromatic number3
Chromatic index4
PropertiesCubic
Strongly regular
Snark
Pappus graph
Named afterPappus of Alexandria
Vertices18
Edges27
PropertiesDistance-regular
Cubic
Grötzsch graph
Named afterHerbert Grötzsch
Vertices11
Edges20
Chromatic number4
PropertiesTriangle-free
Desargues graph
Named afterGérard Desargues
Vertices20
Edges30
PropertiesCubic
Distance-regular
Higman–Sims graph

The graph with semi-random vertex position
Named afterDonald G. Higman
Charles C. Sims
Vertices100
Edges1100
PropertiesStrongly regular
N-cycle

A cycle graph of length 6
Verticesn
Edgesn
Chromatic number3 if n is odd
2 if n is even
Properties2-regular
Unit distance
Kneser graph

The Petersen graph is a Kneser graph
Named afterMartin Kneser
PropertiesArc-transitive
Null graph
Vertices0
Edges0
Hypercube graph

The hypercube graph Q4
Vertices2n
Edges2n−1n
PropertiesArc-transitive
Unit distance
Order-n dipole graph
Vertices2
Edgesn
Foster graph
Paley graph

The Paley graph of order 13
Named afterRaymond Paley
PropertiesStrongly regular
Szekeres snark
Named afterGeorge Szekeres
Vertices50
PropertiesSnark
Turán graph

The Turán graph T(13,4)
Named afterPál Turán
Tutte–Coxeter graph
Named afterW. T. Tutte
H. S. M. Coxeter
Vertices30
Edges45
Girth8
PropertiesCubic
Cage
Moore graph
Bipartite
Arc-transitive
Wheel graph

Several examples of wheel graphs
Verticesn
Edges2(n − 1)
Chromatic number3 if n is odd
4 if n is even
Complete graph

K7, a complete graph with 7 vertices
Verticesn
Edgesn(n − 1) / 2
Gray graph
Named afterMarion Cameron Gray
Vertices54
Girth8
PropertiesCubic
Semi-symmetric
Bipartite
Heawood graph
Vertices14
Edges21
Girth6
PropertiesCubic
Cage
Distance-regular
Toroidal