A graph that encodes local operations in mathematics
The flip graphs of a quadrilateral (top-left), a pentagon (top-right), and a hexagon (bottom).Examples of flips in dimension 1 (top-right), 2 (top-left and central row), and 3 (bottom row).
In mathematics, a flip graph is a graph whose vertices are combinatorial or geometric objects, and whose edges link two of these objects when they can be obtained from one another by an elementary operation called a flip. Flip graphs are special cases of geometric graphs.
Among noticeable flip graphs, one finds the 1-skeleton of polytopes such as associahedra[1] or cyclohedra.[2]
^Lee, Carl (1989), "The Associahedron and Triangulations of the -gon", European Journal of Combinatorics, 10 (6): 551–560, doi:10.1016/S0195-6698(89)80072-1, MR 1022776
^Simion, Rodica (2003), "A type-B associahedron", Advances in Applied Mathematics, 30 (1–2): 2–25, doi:10.1016/S0196-8858(02)00522-5, MR 1979780
an elementary operation called a flip. Flipgraphs are special cases of geometric graphs. Among noticeable flipgraphs, one finds the 1-skeleton of polytopes...
classes of graphs including median graphs have related definitions involving metric embeddings (Bandelt & Chepoi 2008). A flipgraph is a graph formed from...
Cayley graphs on nilpotent groups with cyclic commutator subgroup are Hamiltonian. The flipgraph of a convex polygon or equivalently, the rotation graph of...
cases, as it is conditioned to the connectedness of the underlying flipgraph: this graph is connected for two-dimensional sets of points, but may be disconnected...
Retrieved 21 January 2018. Coxeter 1970, p. 18. Pournin, Lionel (2013), "The flip-Graph of the 4-dimensional cube is connected", Discrete & Computational Geometry...
polygons of pre-specified shapes. Nonzero-rule Catalan number Planar graphFlipgraph Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf...
distance in a flipgraph, a graph that has a vertex for each triangulation and an edge for each flip between two triangulations. Flips and flip distances...
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it...
preserving the property that the orientation is strong. Therefore, the flipgraph whose vertices correspond to the strong orientations of G, and whose edges...
PSPACE-complete. Rotation distance in binary trees and related problems of flip distance in flipgraphs. A rotation is an operation that changes the structure of a binary...
polytope whose definition allows parentheses to wrap around in cyclic order. Flipgraph, a generalisation of the 1-skeleton of the associahedron. Permutohedron...
at any point in the stack and used to flip all pancakes above it. A pancake number is the minimum number of flips required for a given number of pancakes...
distance in a flipgraph, a graph that has a vertex for each triangulation and an edge for each flip between two triangulations. Flips and flip distances...
{\displaystyle N} but the isomorphism does not preserve the triangulation. Flipgraph Unknotting problem Pachner, Udo (1991), "P.L. homeomorphic manifolds are...
In the mathematical field of graph theory, the pancake graph Pn or n-pancake graph is a graph whose vertices are the permutations of n symbols from 1 to...
permutohedron. The graph made up of the vertices and edges of the d {\displaystyle d} -dimensional cyclohedron is the flipgraph of the centrally symmetric...
combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory...
football teams use a three-way coin flip. A legacy of that particular 1988 coin flip was to reduce the use of coin flips to break ties in Texas sports, instead...
A bond graph is a graphical representation of a physical dynamic system. It allows the conversion of the system into a state-space representation. It...
moved one unit to the left. After five flips, the marker could now be on -5, -3, -1, 1, 3, 5. With five flips, three heads and two tails, in any order...
permutations, the 1-skeleton of the permutoassociahedron is a flipgraph with two different kinds of flips (associativity and transpositions). Permutohedron Associahedron...
The Google Knowledge Graph is a knowledge base from which Google serves relevant information in an infobox beside its search results. This allows the...
mathematical field of graph theory, a prism graph is a graph that has one of the prisms as its skeleton. The individual graphs may be named after the...
} {\displaystyle \{H\}} occurs if a head is flipped, and { T } {\displaystyle \{T\}} if a tail is flipped. For this particular coin, it is assumed that...
either pendulum to flip. Outside this region, the pendulum can flip, but it is a complex question to determine when it will flip. Similar behavior is...
graph is, in graph theory, a hypohamiltonian graph with 16 vertices and 27 edges. It has book thickness 3 and queue number 2. Hypohamiltonian graphs were...
learners and concepts is through a bipartite graph. Directed graph of learners and concepts, where a graph that includes both learner and concept nodes...
16-vertex graphs. There exist at least thirteen 18-vertex hypohamiltonian graphs. By applying the flip-flop method of Chvátal (1973) to the Petersen graph and...
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