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The game is played on a finite graph with two special nodes, A and B. Each edge of the graph can be either colored or removed. The two players are called Short and Cut, and alternate moves. On Cut's turn, Cut deletes from the graph a non-colored edge of their choice. On Short's turn, Short colors any edge still in the graph.
In the mathematical field of graph theory, Fáry's theorem states that any simple, planar graph can be drawn without crossings so that its edges are straight line segments. That is, the ability to draw graph edges as curves instead of as straight line segments does not allow a larger class of graphs to be drawn.
A loop is an edge that joins a vertex to itself. Graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex to itself is the edge (for an undirected simple graph) or is incident on (for an undirected multigraph) {,} = {} which is not in {{,},}. To allow loops, the definitions must be expanded.
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011.
SageMath is designed partially as a free alternative to the general-purpose mathematics products Maple and MATLAB. It can be downloaded or used through a web site. SageMath comprises a variety of other free packages, with a common interface and language. SageMath is developed in Python.
A cycle graph or circular graph of order n ≥ 3 is a graph in which the vertices can be listed in an order v 1, v 2, …, v n such that the edges are the {v i, v i+1} where i = 1, 2, …, n − 1, plus the edge {v n, v 1}. Cycle graphs can be characterized as connected graphs in which the degree of all vertices is 2.
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The Farey diagram of any set of rational numbers is a planar graph, and the Farey diagram of the set of all rational numbers forms a tessellation of the hyperbolic plane by ideal triangles. [11] Arc diagrams or circuit diagrams are commonly used in studying folded biopolymers such as proteins and nucleic acids (DNAs, RNAs). Biopolymers are ...