| dbo:abstract |
En théorie des graphes, un graphe zéro-symétrique est un graphe cubique tel que pour tout couple de sommets, il existe un unique automorphisme envoyant le premier sur le second. On parle également de représentation graphique régulière cubique (GRR, pour Graphical Regular Representation) d'un groupe G lorsque le groupe des automorphismes du graphe zéro-symétrique est isomorphe à G. (fr) In the mathematical field of graph theory, a zero-symmetric graph is a connected graph in which each vertex has exactly three incident edges and, for each two vertices, there is a unique symmetry taking one vertex to the other. Such a graph is a vertex-transitive graph but cannot be an edge-transitive graph: the number of symmetries equals the number of vertices, too few to take every edge to every other edge. The name for this class of graphs was coined by R. M. Foster in a 1966 letter to H. S. M. Coxeter. In the context of group theory, zero-symmetric graphs are also called graphical regular representations of their symmetry groups. (en) |
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dbc:Graph_families dbr:Vertex-transitive_graph dbc:Regular_graphs dbr:Connected_graph dbr:Mathematics dbc:Algebraic_graph_theory dbr:Truncated_cuboctahedron dbr:R._M._Foster dbr:Edge-transitive_graph dbr:Cayley_graph dbr:Graph_automorphism dbr:Graph_theory dbr:Harold_Scott_MacDonald_Coxeter dbr:LCF_notation dbr:Bipartite_graph dbr:Planar_graph dbr:Group_theory dbr:Lovász_conjecture dbr:Semi-symmetric_graph dbr:Hamiltonian_cycle dbr:Combinatorial_enumeration dbr:Truncated_cuboctahedral_graph dbr:Truncated_icosidodecahedral_graph dbr:File:Two-edge-orbit_GRR.svg |
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right (en) |
| dbp:alt |
18 (xsd:integer) Truncated cuboctahedron (en) |
| dbp:caption |
The truncated cuboctahedron, a zero-symmetric polyhedron (en) The smallest zero-symmetric graph, with 18 vertices and 27 edges (en) |
| dbp:direction |
horizontal (en) |
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18 (xsd:integer) Great rhombicuboctahedron.png (en) |
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200 (xsd:integer) |
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dbc:Graph_families dbc:Regular_graphs dbc:Algebraic_graph_theory |
| rdfs:comment |
En théorie des graphes, un graphe zéro-symétrique est un graphe cubique tel que pour tout couple de sommets, il existe un unique automorphisme envoyant le premier sur le second. On parle également de représentation graphique régulière cubique (GRR, pour Graphical Regular Representation) d'un groupe G lorsque le groupe des automorphismes du graphe zéro-symétrique est isomorphe à G. (fr) In the mathematical field of graph theory, a zero-symmetric graph is a connected graph in which each vertex has exactly three incident edges and, for each two vertices, there is a unique symmetry taking one vertex to the other. Such a graph is a vertex-transitive graph but cannot be an edge-transitive graph: the number of symmetries equals the number of vertices, too few to take every edge to every other edge. (en) |
| rdfs:label |
Graphe zéro-symétrique (fr) Zero-symmetric graph (en) |
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freebase:Zero-symmetric graph yago-res:Zero-symmetric graph wikidata:Zero-symmetric graph dbpedia-fr:Zero-symmetric graph dbpedia-hu:Zero-symmetric graph https://global.dbpedia.org/id/2Nf7v |
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wikipedia-en:Zero-symmetric_graph |
