Search results
Results from the WOW.Com Content Network
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 ...
Compared to a directed-graph representation, a Hasse diagram needs fewer edges, leading to a less tangled image. Since the relation "a directed path exists from x to y" is transitive, only transitive relations can be represented in Hasse diagrams. Usually the diagram is laid out such that all edges point in an upward direction, and the arrows ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
The path or series of states through which a system passes from an initial equilibrium state to a final equilibrium state [1] and can be viewed graphically on a pressure-volume (P-V), pressure-temperature (P-T), and temperature-entropy (T-s) diagrams. [2] There are an infinite number of possible paths from an initial point to an end point in a ...
[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.