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37 relations: Archimedean solid, Bipartite graph, Cayley graph, Complement graph, Connectivity (graph theory), Countable set, Cube-connected cycles, Edge-transitive graph, Euclidean tilings by convex regular polygons, Free group, Frucht graph, Graduate Texts in Mathematics, Graph (discrete mathematics), Graph automorphism, Graph theory, Group action, Heawood graph, If and only if, Imre Leader, Line graph, List of convex uniform tilings, Lovász conjecture, Mathematics, Metric (mathematics), Path (graph theory), Petersen graph, Platonic solid, Rado graph, Regular graph, Semi-symmetric graph, Symmetric graph, Tessellation, Tietze's graph, Tree (graph theory), Truncated tetrahedron, Uniform tiling, Zero-symmetric graph.
Archimedean solid
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.
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Bipartite graph
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph.
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Cayley graph
In mathematics, a Cayley graph, also known as a Cayley colour graph, Cayley diagram, group diagram, or colour group is a graph that encodes the abstract structure of a group.
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Complement graph
In graph theory, the complement or inverse of a graph is a graph on the same vertices such that two distinct vertices of are adjacent if and only if they are not adjacent in.
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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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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Cube-connected cycles
In graph theory, the cube-connected cycles is an undirected cubic graph, formed by replacing each vertex of a hypercube graph by a cycle.
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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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Euclidean tilings by convex regular polygons
Euclidean plane tilings by convex regular polygons have been widely used since antiquity.
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Free group
In mathematics, the free group FS over a given set S consists of all expressions (a.k.a. words, or terms) that can be built from members of S, considering two expressions different unless their equality follows from the group axioms (e.g. st.
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Frucht graph
In the mathematical field of graph theory, the Frucht graph is a 3-regular graph with 12 vertices, 18 edges, and no nontrivial symmetries.
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Graduate Texts in Mathematics
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.
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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 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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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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If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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Imre Leader
Imre Bennett Leader is a British mathematician and Othello player.
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Line graph
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. The name line graph comes from a paper by although both and used the construction before this.
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List of convex uniform tilings
This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings.
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Lovász conjecture
In graph theory, the Lovász conjecture (1969) is a classical problem on Hamiltonian paths in graphs.
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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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Metric (mathematics)
In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set.
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Path (graph theory)
In graph theory, a path in a graph is a finite or infinite sequence of edges which connect a sequence of vertices which, by most definitions, are all distinct from one another.
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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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Platonic solid
In three-dimensional space, a Platonic solid is a regular, convex polyhedron.
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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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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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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).
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Tessellation
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
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Tietze's graph
In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges.
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Tree (graph theory)
In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path.
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Truncated tetrahedron
In geometry, the truncated tetrahedron is an Archimedean solid.
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Uniform tiling
In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive.
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Zero-symmetric graph
In the mathematical field of graph theory, a zero-symmetric graph is a connected graph in which all vertices are symmetric to each other, each vertex has exactly three incident edges, and these three edges are not symmetric to each other.
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References
[1] https://en.wikipedia.org/wiki/Vertex-transitive_graph
