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In the mathematical field of graph theory, the ladder graph L n is a planar, undirected graph with 2n vertices and 3n – 2 edges. [ 1 ] The ladder graph can be obtained as the Cartesian product of two path graphs , one of which has only one edge: L n ,1 = P n × P 2 .
A quartic equation has four solutions, and only one solution for this equation matches the problem as presented. Another solution is for a case where one ladder (and wall) is below ground level and the other above ground level. In this case the ladders do not actually cross, but their extensions do so at the specified height.
In this diagram, the juggler threw a 3, so an x goes in the third spot, replacing the -, and we have x-xx- as the new state. The diagram shown illustrates all possible states for someone juggling three items and a maximum height of 5. From each state one can follow the arrows and the corresponding numbers produce the siteswap.
In graph theory, the Möbius ladder M n, for even numbers n, is formed from an n-cycle by adding edges (called "rungs") connecting opposite pairs of vertices in the cycle. It is a cubic, circulant graph, so-named because (with the exception of M 6 (the utility graph K 3,3), M n has exactly n/2 four-cycles [1] which link together by their shared edges to form a topological Möbius strip.
In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
Ladder diagram may refer to: Message sequence chart, in Unified Modeling Language (UML) Ladder logic, a method of drawing electrical logic schematics. A ladder diagram represents a program in ladder logic. A method of juggling notation; One type of Feynman diagram
Part of a ladder diagram, including contacts and coils, compares, timers and monostable multivibrators. Ladder logic is widely used to program PLCs, where sequential control of a process or manufacturing operation is required. Ladder logic is useful for simple but critical control systems or for reworking old hardwired relay circuits. As ...
The balanced form of ladder topology can be viewed as being the graph of the side of a prism of arbitrary order. The side of an antiprism forms a topology which, in this sense, is an anti-ladder. Anti-ladder topology finds an application in voltage multiplier circuits, in particular the Cockcroft-Walton generator. There is also a full-wave ...