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Symmetric graph

Index Symmetric graph

In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of G, there is an automorphism such that In other words, a graph is symmetric if its automorphism group acts transitively upon ordered pairs of adjacent vertices (that is, upon edges considered as having a direction). [1]

46 relations: Algebraic graph theory, American Institute of Electrical Engineers, Bell Labs, Complete bipartite graph, Complete graph, Connectivity (graph theory), Coxeter graph, Cube, Cubic graph, Cuboctahedron, Cycle graph, Desargues graph, Distance (graph theory), Distance-transitive graph, Dodecahedron, Dyck graph, Edge-transitive graph, F26A graph, Foster graph, Generalized Petersen graph, Girth (graph theory), Graph (discrete mathematics), Graph automorphism, Graph theory, Group (mathematics), Group action, Half-transitive graph, Heawood graph, Holt graph, Hypercube graph, Icosahedron, Icosidodecahedron, Marston Conder, Mathematics, Möbius–Kantor graph, Nauru graph, Octahedron, Pappus graph, Petersen graph, R. M. Foster, Rado graph, Regular graph, Regular map (graph theory), Semi-symmetric graph, Tutte–Coxeter graph, Vertex-transitive graph.

Algebraic graph theory

Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs.

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American Institute of Electrical Engineers

The American Institute of Electrical Engineers (AIEE) was a United States-based organization of electrical engineers that existed from 1884 through 1962.

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Bell Labs

Nokia Bell Labs (formerly named AT&T Bell Laboratories, Bell Telephone Laboratories and Bell Labs) is an American research and scientific development company, owned by Finnish company Nokia.

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Complete bipartite graph

No description.

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Complete graph

No description.

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Connectivity (graph theory)

In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to disconnect the remaining nodes from each other.

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Coxeter graph

In the mathematical field of graph theory, the Coxeter graph is a 3-regular graph with 28 vertices and 42 edges.

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Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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Cubic graph

In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three.

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Cuboctahedron

In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.

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Cycle graph

In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices connected in a closed chain.

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Desargues graph

In the mathematical field of graph theory, the Desargues graph is a distance-transitive cubic graph with 20 vertices and 30 edges.

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Distance (graph theory)

In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them.

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Distance-transitive graph

In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y.

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Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

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Dyck graph

In the mathematical field of graph theory, the Dyck graph is a 3-regular graph with 32 vertices and 48 edges, named after Walther von Dyck.

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Edge-transitive graph

In the mathematical field of graph theory, an edge-transitive graph is a graph G such that, given any two edges e1 and e2 of G, there is an automorphism of G that maps e1 to e2.

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F26A graph

In the mathematical field of graph theory, the F26A graph is a symmetric bipartite cubic graph with 26 vertices and 39 edges.

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Foster graph

In the mathematical field of graph theory, the Foster graph is a bipartite 3-regular graph with 90 vertices and 135 edges.

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Generalized Petersen graph

In graph theory, the generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon.

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Girth (graph theory)

In graph theory, the girth of a graph is the length of a shortest cycle contained in the graph.

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Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

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Graph automorphism

In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the edge–vertex connectivity.

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Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

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Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

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Group action

In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

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Half-transitive graph

In the mathematical field of graph theory, a half-transitive graph is a graph that is both vertex-transitive and edge-transitive, but not symmetric.

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Heawood graph

In the mathematical field of graph theory, the Heawood graph is an undirected graph with 14 vertices and 21 edges, named after Percy John Heawood.

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Holt graph

In the mathematical field of graph theory, the Holt graph or Doyle graph is the smallest half-transitive graph, that is, the smallest example of a vertex-transitive and edge-transitive graph which is not also symmetric.

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Hypercube graph

In graph theory, the hypercube graph is the graph formed from the vertices and edges of an -dimensional hypercube.

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Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

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Icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces.

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Marston Conder

Marston Donald Edward Conder (born September 1955) is a New Zealand mathematician, a Distinguished Professor of Mathematics at Auckland University,, Auckland U. Mathematics, retrieved 2013-01-22.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Möbius–Kantor graph

In the mathematical field of graph theory, the Möbius–Kantor graph is a symmetric bipartite cubic graph with 16 vertices and 24 edges named after August Ferdinand Möbius and Seligmann Kantor.

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Nauru graph

In the mathematical field of graph theory, the Nauru graph is a symmetric bipartite cubic graph with 24 vertices and 36 edges.

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Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

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Pappus graph

In the mathematical field of graph theory, the Pappus graph is a bipartite 3-regular undirected graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus configuration.

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Petersen graph

In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges.

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R. M. Foster

Ronald Martin Foster (3 October 1896 – 2 February 1998), was a Bell Labs mathematician whose work was of significance regarding electronic filters for use on telephone lines.

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Rado graph

In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with probability one) by choosing independently at random for each pair of its vertices whether to connect the vertices by an edge.

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Regular graph

In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency.

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Regular map (graph theory)

In mathematics, a regular map is a symmetric tessellation of a closed surface.

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Semi-symmetric graph

In the mathematical field of graph theory, a semi-symmetric graph is an undirected graph that is edge-transitive and regular, but not vertex-transitive.

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Tutte–Coxeter graph

In the mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage is a 3-regular graph with 30 vertices and 45 edges.

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Vertex-transitive graph

In the mathematical field of graph theory, a vertex-transitive graph is a graph G such that, given any two vertices v1 and v2 of G, there is some automorphism such that In other words, a graph is vertex-transitive if its automorphism group acts transitively upon its vertices.

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Arc-transitive, Arc-transitive graph, Flag-transitive graph, Foster Census, Foster census.

References

[1] https://en.wikipedia.org/wiki/Symmetric_graph

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