An aperiodic graph. The cycles in this graph have lengths 5 and 6; therefore, there is no k > 1 that divides all cycle lengths.A strongly connected graph with period three.
In the mathematical area of graph theory, a directed graph is said to be aperiodic if there is no integer k > 1 that divides the length of every cycle of the graph. Equivalently, a graph is aperiodic if the greatest common divisor of the lengths of its cycles is one; this greatest common divisor for a graph G is called the period of G.
area of graph theory, a directed graph is said to be aperiodic if there is no integer k > 1 that divides the length of every cycle of the graph. Equivalently...
acyclic graph, a directed graph with no cycles Strongly connected graph, a directed graph in which every edge belongs to a cycle Aperiodicgraph, a directed...
methods for constructing aperiodic tilings are known. Consider a periodic tiling by unit squares (it looks like infinite graph paper). Now cut one square...
combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory...
that exhibit periodicity. Any function that is not periodic is called aperiodic. A function f is said to be periodic if, for some nonzero constant P,...
then this set of tiles is called aperiodic. The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly speaking...
In mathematics, an aperiodic semigroup is a semigroup S such that every element is aperiodic, that is, for each x in S there exists a positive integer...
called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern (an aperiodic set of prototiles). A tessellation...
problem can be stated briefly as: Every finite strongly connected aperiodicgraph of uniform out-degree has a synchronizing coloring. Previous partial...
example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does...
power method to converge, the matrix must be stochastic, irreducible and aperiodic. In order to generate the Google matrix G, we must first generate an adjacency...
regularly at a constant period. The term can also be used for non-periodic or aperiodic signals, like chirps and pulses. In electronics, the term is usually applied...
acyclic finite state automaton (DAFSA), also called a directed acyclic word graph (DAWG; though that name also refers to a related data structure that functions...
following properties: the graph represented by T {\displaystyle T} is aperiodic there is a unique left eigenvector s {\displaystyle s} of T {\displaystyle...
can reach every other state through some sequence of transitions, and aperiodic if, for every state, the possible numbers of steps in sequences that start...
the plane. Regular tetrahedra can be stacked face-to-face in a chiral aperiodic chain called the Boerdijk–Coxeter helix. In four dimensions, all the convex...
the given graph is strongly connected and aperiodic. Ramsey's theorem concerns the problem of k-coloring the edges of a large complete graph Kn in order...
Analysis of aperiodic circuits and asynchronous processes (PhD). Leningrad Electrotechnical Institute. Bryant., Randal E. (1986). "Graph-Based Algorithms...
fundamental result about Markov chains is that a finite state irreducible aperiodic chain has a unique stationary distribution π and, regardless of the initial...
the same period. In particular, if one state is aperiodic, then the whole Markov chain is aperiodic. If a finite Markov chain is irreducible, then all...
In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges. It is a polyhedral graph (the...
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