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Distance-transitive graph

Index 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. [1]

34 relations: Asymptotic analysis, Automorphism, Biggs–Smith graph, Complete bipartite graph, Complete graph, Coxeter graph, Cube, Cubic graph, Desargues graph, Distance (graph theory), Distance-regular graph, Dodecahedron, Finite group, Folded cube graph, Foster graph, Georgy Adelson-Velsky, Girth (graph theory), Graph (discrete mathematics), Graph automorphism, Graph theory, Grassmann graph, Hamming graph, Heawood graph, Hypercube graph, Johnson graph, Mathematics, Norman L. Biggs, Pappus graph, Petersen graph, Proceedings of the USSR Academy of Sciences, Rook's graph, Shrikhande graph, Tutte 12-cage, Tutte–Coxeter graph.

Asymptotic analysis

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.

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Automorphism

In mathematics, an automorphism is an isomorphism from a mathematical object to itself.

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Biggs–Smith graph

In the mathematical field of graph theory, the Biggs–Smith graph is a 3-regular graph with 102 vertices and 153 edges.

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Complete bipartite graph

No description.

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Complete graph

No description.

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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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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-regular graph

In mathematics, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and i.

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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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Finite group

In abstract algebra, a finite group is a mathematical group with a finite number of elements.

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Folded cube graph

In graph theory, a folded cube graph is an undirected graph formed from a hypercube graph by adding to it a perfect matching that connects opposite pairs of hypercube vertices.

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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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Georgy Adelson-Velsky

Georgy Maximovich Adelson-Velsky (Гео́ргий Макси́мович Адельсо́н-Ве́льский; name is sometimes transliterated as Georgii Adelson-Velskii) (8 January 1922 – 26 April 2014) was a Soviet and Israeli mathematician and computer scientist.

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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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Grassmann graph

Grassmann graphs are a special class of simple graphs defined from systems of subspaces.

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Hamming graph

Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics and computer science.

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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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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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Johnson graph

Johnson graphs are a special class of undirected graphs defined from systems of sets.

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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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Norman L. Biggs

Norman Linstead Biggs (born 2 January 1941) is a leading British mathematician focusing on discrete mathematics and in particular algebraic combinatorics.

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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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Proceedings of the USSR Academy of Sciences

The Proceedings of the USSR Academy of Sciences (Доклады Академии Наук СССР, Doklady Akademii Nauk SSSR (DAN SSSR), Comptes Rendus de l'Académie des Sciences de l'URSS) was a Soviet journal that was dedicated to publishing original, academic research papers in physics, mathematics, chemistry, geology, and biology.

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Rook's graph

In graph theory, a rook's graph is a graph that represents all legal moves of the rook chess piece on a chessboard.

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Shrikhande graph

In the mathematical field of graph theory, the Shrikhande graph is a named graph discovered by S. S. Shrikhande in 1959.

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Tutte 12-cage

In the mathematical field of graph theory, the Tutte 12-cage or Benson graph is a 3-regular graph with 126 vertices and 189 edges named after W. T. Tutte.

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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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Redirects here:

Distance transitive graph, Distance-transitive graphs.

References

[1] https://en.wikipedia.org/wiki/Distance-transitive_graph

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