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In the mathematical field of graph theory, a path graph (or linear graph) is a graph whose vertices can be listed in the order v 1, v 2, ..., v n such that the edges are {v i, v i+1} where i = 1, 2, ..., n − 1. Equivalently, a path with at least two vertices is connected and has two terminal vertices (vertices of degree 1), while all others ...
A three-dimensional hypercube graph showing a Hamiltonian path in red, and a longest induced path in bold black. In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges).
The commutative diagram used in the proof of the five lemma. In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. [1] It is said that commutative diagrams play the role in category theory that equations play in ...
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding ...
A path from x to y exists in the Hasse diagram representing R div. An edge from x to y exists in the directed graph representing R div. In the Boolean matrix representing R div, the element in line x, column y is "". As another example, define the relation R el on R by x R el y if x 2 + xy + y 2 = 1.
The situation is depicted in the symmetric Loedel diagrams of Fig 4-1. Note that we can compare spacetime lengths on page directly with each other, due to the symmetric nature of the Loedel diagram. In Fig 4-2, the observer whose reference frame is given by the black axes is assumed to move from the origin O towards A.
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[1]: 62–63 A world line traces out the path of a single point in spacetime. A world sheet is the analogous two-dimensional surface traced out by a one-dimensional line (like a string) traveling through spacetime. The world sheet of an open string (with loose ends) is a strip; that of a closed string (a loop) resembles a tube.