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Clebsch graph

In the mathematical field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with 80 edges. The 80-edge graph is the dimension-5 halved cube graph; it was called the Clebsch graph by Seidel (1968) because of its relation to the configuration of 16 lines on the…

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Automorphisms
1920
Book thickness
4
Chromatic index
5
Chromatic number
4
Diameter
2
Edges
40

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Construction

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Gallery

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Clebsch graph

Nodes56
Edges55
Triples45
Avg. degree1.96
Density0.035714
Components1

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Clebsch graph

Top relations

related to Algebraic properties · 9
Clebsch graph → As, Because, Cayley, Clebsch, Coxeter, In, It, The, The Clebsch
related to Properties · 7
Clebsch graph → Clebsch, Eulerian, Hamiltonian, It, Its, Petersen, The
is a · 6
Clebsch graph → integral graph, Keller graph of dimension two, only graph with this characteristic polynomial, strongly regular graph of degree 5 with parameters, supergraph of the Grötzsch graph, triangle-free graph
related to Construction · 6
Clebsch graph → Alternatively, Another, Clebsch, GF, In, The
related to Gallery · 5
Clebsch graph → Clebsch, Construction, Hamiltonian, The, The Clebsch
Automorphisms · 1
Clebsch graph → 1920
Book thickness · 1
Clebsch graph → 4
Chromatic index · 1
Clebsch graph → 5
Chromatic number · 1
Clebsch graph → 4
Diameter · 1
Clebsch graph → 2

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Important terminology

graph clebsch 5-regular vertices two 16 edges number cube hamiltonian hypercube also strongly regular dimension-5 construction graphs 10-regular cayley gleason

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Clebsch graphAutomorphisms19201.00infobox
Clebsch graphBook thickness41.00infobox
Clebsch graphChromatic index51.00infobox
Clebsch graphChromatic number41.00infobox
Clebsch graphDiameter21.00infobox
Clebsch graphEdges401.00infobox
Clebsch graphGirth41.00infobox
Clebsch graphNamed afterAlfred Clebsch1.00infobox
Clebsch graphPropertiesStrongly regular Hamiltonian Cayley graph Vertex-transitive Edge-transitive Distance-transitive.1.00infobox
Clebsch graphQueue number31.00infobox
Clebsch graphRadius21.00infobox
Clebsch graphVertices161.00infobox
Clebsch graphis astrongly regular graph of degree 5 with parameters0.90text
Clebsch graphis atriangle-free graph0.90text
Clebsch graphis asupergraph of the Grötzsch graph0.90text
Clebsch graphis aKeller graph of dimension two0.90text
Clebsch graphis aintegral graph0.90text
Clebsch graphis aonly graph with this characteristic polynomial0.90text

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